Дисертації з теми "Nonlinear Structural Dynamic"

The identification of linear structural dynamic systems has been dealt with extensively in past studies. Identification methods for nonlinear structures have also been introduced in previous articles, including procedures based on the method of multiple scales, iterative and noniterative direct methods, and state space mappings. Here, a procedure is introduced for the identification of nonlinear structural dynamic systems which is readily applicable to simple as well as more complex multiple degree of freedom systems. The procedure is based on multiple step integration methods for the solution of differential equations. The multiple step integration procedure and the iterative direct method are applied to a number of nonlinear single degree of freedom examples, and are applied to a simple two degrees of freedom example as well. RMS based noise is added to a simulated measured response in order to monitor the effects of measurement errors on the procedures. The input data is filtered before final processing in the identification algorithms. The multistep algorithm is compared to the iterative direct method on the basis of criteria such as accuracy, ease of use, and numerical efficiency.
Master of Science

The present work describes the finite element (FE) modeling and dynamic response of lightweight, deployable shelters (tent) to large external blast loads. Flexible shelters have been used as temporary storage places for housing equipments, vehicles etc. TEMPER Tents, Small Shelter System have been widely used by Air Force and Army, for various field applications. These shelters have pressurized Collective Protection System (CPS), liner, fitted to the frame structure, which can provide protection against explosives and other harmful agents. Presently, these shelter systems are being tested for the force protection standards against the explosions like air-blast. In the field tests carried out by Air Force Research Laboratory, it was revealed that the liner fitted inside the tent was damaged due to the air blast explosion at some distant from the structure, with major damage being on the back side of the tent. The damage comprised of tearing of liner and separation of zip seals. To investigate the failure, a computational approach, due to its simplicity and ability to solve the complex problems, is used. The response of any structural form to dynamic loading condition is very difficult to predict due to its dependence on multiple factors like the duration of the loading, peak load, shape of the pulse, the impulse energy, boundary conditions and material properties etc. And dynamic analysis of shell structures pose even much greater challenge. Obtaining solution analytically presents a very difficult preposition when nonlinearity is considered. Therefore, the numerical approach is sought which provide simplicity and comparable accuracy. A 3D finite element model has been developed, consisting of fabric skin supported over the frames based on two approaches. ANSYS has been used for obtaining the dynamic response of shelter against the blast loads. In the first approach, the shell is considered as a membrane away from its boundaries, in which the stress couple is neglected in its interior region. In the second approach, stress coupling is neglected over the whole region. Three models were developed using Shell 63, Shell 181 and Shell 41. Shell 63 element supports both the membrane only and membrane-bending combined options and include stress stiffening and large deflection capabilities. Shell 181 include all these options as Shell 63 does and also, accounts for the follower loads. Shell 41 is a membrane element and does not include any bending stiffness. This element also include stress stiffening and large deflection capabilities. A nonlinear static analysis is performed for a simple plate model using the elements, Shell 41 and Shell 63. The membrane dominated behavior is observed for the shell model as the pressure load is increased. It is also observed that the higher value of Young's modulus (E) increases the stresses significantly. Transient analysis is a method of determining the structural response due to time dependent loading conditions. The full method has been used for performing the nonlinear transient analysis. Its more expensive in terms of computation involved but it takes into account all types of nonlinearities such as plasticity, large deflection and large strain etc. Implicit approach has been used where Newmark method along with the Newton-Raphson method has been used for the nonlinear analysis. Dynamic response comprising of displacement-time history and dynamic stresses has been obtained. From the displacement response, it is observed that the first movement of the back wall is out of the tent in contrast to the other sides whose first movement is into the tent. Dynamic stresses showed fluctuations in the region when the blast is acting on the structure and in the initial free vibration zone. A parametric study is performed to provide insight into the design criteria. It is observed that the mass could be an effective means of reducing the peak responses. As the value of the Young's Modulus (E) is increased, the peak displacements are reduced resulting from the increase in stiffness. The increased stiffness lead to reduced transmitted peak pressure and reduced value of maximum strain. But a disproportionate increase lead to higher stresses which could result in failure. Therefore, a high modulus value should be avoided.
Master of Science

The analysis of stiffened plate structures subject to complex loads such as air-blast pressure waves from external or internal explosions, water waves, collisions or simply large static loads is still considered a difficult task. The associated response is highly nonlinear and although it can be solved with currently available commercial finite element programs, the modelling requires many elements with a huge amount of input data and very expensive computer runs. Hence this type of analysis is impractical at the preliminary design stage. The present work is aimed at improving this situation by introducing a new philosophy. That is, a new formulation is developed which is capable of representing the overall response of the complete structure with reasonable accuracy but with a sacrifice in local detailed accuracy. The resulting modelling is relatively simple thereby requiring much reduced data input and run times. It now becomes feasible to carry out design oriented response analyses. Based on the above philosophy, new plate and stiffener beam finite elements are developed for the nonlinear static and dynamic analysis of stiffened plate structures. The elements are specially designed to contain all the basic modes of deformation response which occur in stiffened plates and are called super finite elements since only one plate element per bay or one beam element per span is needed to achieve engineering design level accuracy at minimum cost. Rectangular plate elements are used so that orthogonally stiffened plates can be modelled. The von Karman large deflection theory is used to model the nonlinear geometric behaviour. Material nonlinearities are modelled by von Mises yield criterion and associated flow rule using a bi-linear stress-strain law. The finite element equations are derived using the virtual work principle and the matrix quantities are evaluated by Gauss quadrature. Temporal integration is carried out using the Newmark-β method with Newton-Raphson iteration for the nonlinear equations at each time step. A computer code has been written to implement the theory and this has been applied to the static, vibration and transient analysis of unstiffened plates, beams and plates stiffened in one or two orthogonal directions. Good approximations have been obtained for both linear and nonlinear problems with only one element representations for each plate bay or beam span with significant savings in computing time and costs. The displacement and stress responses obtained from the present analysis compare well with experimental, analytical or other numerical results.
Applied Science, Faculty of
Civil Engineering, Department of
Graduate

Beams are structural members with one dimension much larger than the other two. Examples of beams include propeller blades, helicopter rotor blades, and high aspect-ratio aircraft wings in aerospace engineering; shafts and wind turbine blades in mechanical engineering; towers, highways and bridges in civil engineering; and DNA modeling in biomedical engineering. Beam analysis includes two sets of equations: a generally linear two-dimensional problem over the cross-sectional plane and a nonlinear, global one-dimensional analysis. This research work deals with a relatively new set of equations for one-dimensional beam analysis, namely the so-called fully intrinsic equations. Fully intrinsic equations comprise a set of geometrically exact, nonlinear, first-order partial differential equations that is suitable for analyzing initially curved and twisted anisotropic beams. A fully intrinsic formulation is devoid of displacement and rotation variables, making it especially attractive because of the absence of singularities, infinite-degree nonlinearities, and other undesirable features associated with finite rotation variables. In spite of the advantages of these equations, using them with certain boundary conditions presents significant challenges. This research work will take a broad look at these challenges of modeling various boundary conditions when using the fully intrinsic equations. Hopefully it will clear the path for wider and easier use of the fully intrinsic equations in future research. This work also includes application of fully intrinsic equations in structural analysis of joined-wing aircraft, different rotor blade configuration and LCO analysis of HALE aircraft.

Deficient concrete structures are serious danger in seismic zones. In order to minimize economical and human loss, these structures should be retrofitted. Selecting suitable retrofitting schemes requires detailed investigation of these systems. Considering these facts, this study aims to calibrate analytical models of systems with chevron braces and internal steel frames
and evaluate their seismic performances. First, analytical models of the frames with braces and internal steel frames were prepared and then their responses were compared with cyclic responses of experimental studies. Results of these models were used to determine performance limits by the methods proposed by TEC2007 and ASCE/SEI-41. Then, calibrated models were employed for time history analyses with various scales of Duzce ground motion and analytical results were compared with experimental findings. Seismic performance of these systems was also evaluated by using aforementioned codes. Finally, evaluated retrofitting schemes were applied to a 4-story 3-bay reinforced concrete frame that was obtained from an existing deficient structure and effectiveness of applied retrofitting schemes was investigated in detail.

Recent advancements in earthquake engineering have caused a movement toward a probabilistic quantification of the behavior of structural systems. Analysis characteristics, such as ground motion records, material properties, and structural component behavior are defined by probabilistic distributions. The response is also characterized probabilistically, with distributions fitted to analysis results at intensity levels ranging from the maximum considered earthquake ground motion to collapse. Despite the progress toward a probabilistic framework, the variability in structural analysis results due to modeling techniques has not been considered. This work investigates the uncertainty associated with modeling geometric nonlinearities and Rayleigh damping models on the response of planar frames at multiple ground motion intensity levels. First, an investigation is presented on geometric nonlinearity approaches for planar frames, followed by a critical review of current damping models. Three frames, a four-story buckling restrained braced frame, a four-story steel moment resisting frame, and an eight-story steel moment resisting frame, are compared using two geometric nonlinearity approaches and five Rayleigh damping models. Static pushover analyses are performed on the models in the geometric nonlinearities study, and incremental dynamic analyses are performed on all models to compare the response at the design based earthquake ground motion (DBE), maximum considered earthquake ground motion (MCE), and collapse intensity levels. The results indicate noticeable differences in the responses at the DBE and MCE levels and significant differences in the responses at the collapse level. Analysis of the sidesway collapse mechanisms indicates a shift in the behavior corresponding to the different modeling assumptions, though the effects were specific to each frame. The FEMA P-695 Methodology provided a framework that defined the static and dynamic analyses performed during the modeling uncertainties studies. However, the Methodology is complex and the analyses are computationally expensive. To expedite the analyses and manage the results, a toolkit was created that streamlines the process using a set of interconnected modules. The toolkit provides a program that organizes data and reduces mistakes for those familiar with the process while providing an educational tool for novices of the Methodology by stepping new users through the intricacies of the process. The collapse margin ratio (CMR), calculated in the Methodology, was used to compare the collapse behavior of the models in the modeling uncertainties study. Though it provides a simple scalar quantity for comparison, calculation of the CMR typically requires determination of the full set of incremental dynamic analysis curves, which require prohibitively large analysis time for complex models. To reduce the computational cost of calculating the CMR, a new parallel computing method, referred to as the fragility search method, was devised that uses approximate collapse fragility curves to quickly converge on the median collapse intensity value. The new method is shown to have favorable attributes compared to other parallel computing methods for determining the CMR.
Ph. D.

Most engineering structures include nonlinearity to some degree. Depending on the dynamic conditions and level of external forcing, sometimes a linear structure assumption may be justified. However, design requirements of sophisticated structures such as satellites, stabilized weapon systems and radars may require nonlinear behavior to be considered for better performance. Therefore, it is very important to successfully detect, localize and parametrically identify nonlinearity in such cases. In engineering applications, the location of nonlinearity and its type may not be always known in advance. Furthermore, as the structure will be excited from only a few coordinates, the frequency response function matrices will not be complete. In order to parametrically identify more than one type of nonlinearity which may co-exist at the same location with the above mentioned limitations, a method is proposed where restoring force surface plots are used which are evaluated by describing function inversion. Then, by reformulating this method, a second method is proposed which can directly evaluate the total describing function of more than one type of nonlinearity which may co-exist at the same location without using any linear frequency response function matrix. It is also aimed in this study to use the nonlinearity localization formulations for damage localization purposes. The validation of the methods developed in this study is demonstrated with case studies based on simulated experiments, as well as real experiments with nonlinear structures and it is concluded that the methods are very promising to be used in engineering structures.

The power plant and aerospace industries have been facing a huge loss, due to structural failure. The structural failure occurs due to the presence of the crack in it. Hence, it becomes necessary to monitor the structural health under operating condition. Most of the techniques, for structural health monitoring are used for a specific purpose. Some of these techniques require structure dismantling, which is very much expensive and time consuming. So the vibration based structural health monitoring is advantageous, compared to other techniques. Most of the vibration based Structural Health Monitoring (SHM) approaches, use linear vibration theory. But, these linear vibration based procedures, have inherently low sensitivity to crack. Since crack introduces nonlinearities in the system, their merits in damage detection need to be investigated for SHM. In this thesis, the problem is focused on studying nonlinear dynamics of cracked structures for Structural Health Monitoring. For this, simulations and experiments are performed. The new procedure for the simulation is developed using Matlab-Simulink. It uses the numerical approximation for dynamic compliance operators and a nonlinear model of cracks contact faces interaction to study the dynamic behaviour of the cracked bar. Furthermore, the finite element model of the cracked cantilever bar with crack- tip plasticity is developed and the dynamic behaviour of the elasto-plastic bar is studied. Additionally, numerous experiments are performed to study the dynamics of cantilever bar with the fatigue crack in it. The results from Matlab-Simulink simulation shows the distribution of higher harmonics generated along the bar length, as a function of distance from the crack. In finite element simulation, comparison is made between the resonance frequency of cracked cantilever bar with and without crack-tip plasticity. It is found that, there is decrease in resonance frequency of the cracked bar with cracked tip plasticity, when compared with the resonance frequency of cracked bar without crack-tip plasticity. This reduction in resonance frequency is due to the crack-induced plasticity near the crack tip which affects the overall stiffness of bar. In experiments, the response is measured at four different points on the cracked cantilever bar at a given resonant frequency of excitation at lower and higher vibration amplitude. For lower vibration amplitude, it is found that the response obtained near the vicinity of the crack shows the presence of higher harmonics of resonant frequency, which disappears in the response obtained far away from the crack. For higher vibration amplitude, it is found that the response obtained near the vicinity of the crack shows the presence of higher harmonics along with the low frequency component. This low frequency component causes modulation, which leads to the generation of side band frequencies near the resonant frequency. The occurrence of low frequency component and side band frequencies is due to the vibro-impact behaviour of crack. The amplitude of these side band frequencies and higher harmonics are reduced in the response obtained far away from the crack. This indicates that crack-induced nonlinearity has a localized effect on the dynamics of bar. It is also observed that the magnitude of low frequency component is proportional to the magnitude of resonant frequency of excitation. This indicates that crack behaves like a signal modulator, detector of low frequency component and amplifier as the magnitude of low frequency component is proportional to the magnitude of resonant frequency excitation. From the Matlab-Simulink simulation and experimental results, it is concluded that crackinduced nonlinearity affects the dynamic behaviour of the cracked bar significantly, which will be effective in structural health monitoring. Keywords: vibro-impact, crack, dynamic compliance, harmonics, modulator, detector, amplifier, crack-tip plasticity, resonance frequency, structural health monitoring.

Experimental nonlinear dynamics is an important area of study in the modern engineering field, with engineering applications in structural dynamics, structural control, and structural health monitoring. As a result, the discipline has experienced a great influx of research efforts to develop a versatile and reliable experimental methodology. A technical challenge in many experimental studies is the procurement of a device that exhibits the desired nonlinear behavior. As a result, many researchers have longed for a versatile, but accurate, testing methodology that has complete freedom to simulate a wide range of nonlinearities and stochastic behaviors. The objective of this study is to develop a reconfigurable test setup as a tool to be used in a wide range of nonlinear dynamic studies. The main components include a moving mass whose restoring force can accurately be controlled and reprogrammed (with software) based upon measured displacement and velocity readings at each time step. The device offers control over nonlinear characteristics and the equation of dynamic motion. The advantage of having such an experimental setup is the ability to simulate various types of nonlinearities with the same test setup. As a result, the data collected can be used to help validate nonlinear modeling, system identification, and stochastic analysis studies. A physical test apparatus was developed, and various mechanical, electrical, and programming calibrations were performed for reliable experimental studies. To display potential uses for the reconfigurable approach, examples are presented where the device has been used to create physical data for use in change detection and deterioration studies. In addition, a demonstration is presented of the device's ability to physically simulate a large-scale orifice viscous damper, devices commonly used for vibration mitigation in bridges and buildings.; For a large-scale viscous damper, physical testing is required to ensure structural design properties. However, due to the large scale of the dampers, expensive dynamic loading tests can be carried out at a very limited number of facilities. Using the reconfigurable test setup, the dynamic signature of the large-scale viscous damper can accurately be simulated with pre-collected data. The development of a system capable of emulating the restoring force of a nonlinear device with software is a novel approach and requires further calibration for increased reliability and accuracy. A discussion regarding the challenges faced when developing the methodology is presented and possible solutions are recommended. The methodology introduced by this apparatus is very promising. The device is a valuable experimental tool for researchers and designers, allowing for physical data collection, modeling, analysis, and validation of a wide class of nonlinear phenomena that commonly occur in a wide variety of engineering applications.
ID: 030423494; System requirements: World Wide Web browser and PDF reader.; Mode of access: World Wide Web.; Thesis (M.S.)--University of Central Florida, 2011.; Includes bibliographical references (p. 132-137).
M.S.
Masters
Civil, Environmental and Construction Engineering
Engineering and Computer Science

Inverse analysis of nonlinear dynamic systems is an important area of research in the ?eld of structural health monitoring for civil engineering structures. Structural damage usually involves localized nonlinear behaviors of dynamic systems that evolve into different classes of nonlinearity as well as change system parameter values. Numerous parametric modal analysis techniques (e.g., eigensystem realization algorithm and subspace identification method) have been developed for system identification of multi-degree-of-freedom dynamic systems. However, those methods are usually limited to linear systems and known for poor sensitivity to localized damage. On the other hand, non-parametric identification methods (e.g., artificial neural networks) are advantageous to identify time-varying nonlinear systems due to unpredictable damage. However, physical interpretation of non-parametric identification results is not as straightforward as those of the parametric methods. In this study, the Multidegree-of-Freedom Restoring Force Method (MRFM) is employed as a semi-parametric nonlinear identification method to take the advantages of both the parametric and non-parametric identification methods. The MRFM is validated using two realistic experimental nonlinear dynamic tests: (i) large-scale shake table tests using building models with different foundation types, and (ii) impact test using wind blades. The large-scale shake table test was conducted at Tongji University using 1:10 scale 12-story reinforced concrete building models tested on three different foundations, including pile, box and fixed foundation. The nonlinear dynamic signatures of the building models collected from the shake table tests were processed using MRFM (i) to investigate the effects of foundation types on nonlinear behavior of the superstructure and (ii) to detect localized damage during the shake table tests. Secondly, the MRFM was applied to investigate the applicability of this method to wind turbine blades. Results are promising, showing a high level of nonlinearity of the system and how the MRFM can be applied to wind-turbine blades. Future studies were planned for the comparison of physical characteristic of this blade with blades created made of other material.
M.S.
Masters
Civil, Environmental, and Construction Engineering
Engineering and Computer Science
Civil Engineering; Structures and Geotechnical Engineering

For repeated transient solutions of geometrically nonlinear structures the numerical effort often poses a major obstacle. Thus, the introduction of a reduced order model, which takes the nonlinear effects into account and accelerates the calculations considerably, is often necessary.This work yields a method that allows for rapid, accurate and parameterisable solutions by means of a reduced model of the original structure. The structure is discretised and its dynamic equilibrium described by a matrix equation. The projection on a reduced basis is introduced to obtain the reduced model. A comprehensive numerical study on several common reduced bases shows that the simple introduction of a constant basis is not sufficient to account for the nonlinear behaviour. Three requirements for an rapid, accurate and parameterisable solution are derived. The solution algorithm has to take into account the nonlinear evolution of the solution, the solution has to be independent of the nonlinear finite element terms and the basis has to be adapted to external parameters.Three approaches are provided, each responding to one requirement. These approaches are assembled to the integrated method. The approaches are the update and augmentation of the basis, the polynomial formulation of the nonlinear terms and the interpolation of the basis. A Newmark-type time-marching algorithm provides the frame of the integrated method. The application of the integrated method on test-cases with geometrically nonlinear finite elements confirms that this method leads to the initial aim of a rapid, accurate and parameterisable transient solution.

In the classical continuum theory of solid mechanics, the mathematical framework involves partial derivatives to represent the state of deformation of a solid body. A significant drawback due to derivatives is related to the unphysical results given near the discontinuities, because they are undefined wherever a continuous field of displacements is not verified, such as in the presence of dislocations, voids, cracks, interfaces between different phases within the same body and grain boundaries. Various techniques were employed for overcoming this incapability of the classical theory in describing material behavior in such conditions; in fact, spontaneous formation and growth of discontinuities are of great importance in solid mechanics: they lead to fractures and failures of systems that must be avoided, especially in aerospace structures, primarily, for safety reasons and, secondly, for economic purposes. One of these new approaches concerns employing nonlocal theories, based on integral formulations (more precisely integro-differential formulations), defined even when non-derivable displacement fields are involved. Peridynamics is one of these theories: it was suggested by Stewart Silling in 2000 [1] in order to adopt a consistent formulation describing material behavior not only when a continuous displacement field is provided, but also whenever discontinuities are present, avoiding partial differential equations or pre-setting of conditions which can influence the results. There are two versions of peridynamic models: bond-based, which was introduced first (see [1, 2]) and state-based. In the bond-based version, forces between two material points depend solely on their relative displacement, their relative initial position, and material properties. Due to its simplicity compared to the state-based version, most of the peridynamic applications have employed bond-based Peridynamics. However, bond-based models result in several limitations (the same of other atomistic or molecular dynamics models [3], although this is a continuum theory, not a discrete one), the most important of these is the fixed value of Poisson’s ratio: 1/4 in 3D or 2D plane strain, and 1/3 in 2D plane stress (see e.g. [1, 4]). This peculiarity implies other restrictions, such as the impossibility of reproducing plastic incompressibility in an accurate way. Nevertheless, for many purposes, bond-based Peridynamics fits the requirements and gives satisfying results. State-based peridynamic models remove these restrictions by allowing the interaction (“bond”) between a pair of points to potentially depend on all other bonds connected to the two points. Moreover, there are two types of state-based peridynamic formulations: ordi- nary and non-ordinary [2, 5, 6]. In the former, the forces between two material points act along the vector connecting the points in the deformed configuration. In the latter, such characteristic is not present. The ordinary state-based formulation requires specific derivation of constitutive models, see examples of viscoelasticity and plasticity models in [7, 8]. For non-ordinary state-based formulation, two approaches have been proposed: the development of an explicit model for the peridynamic force state [2] and the development of a map thanks to which classical mechanics constitutive relations are incorporated to indirectly establish the relationship between the interaction force and the deformation. The latter approach is called correspondence model [2]. The purpose of this thesis has been the investigation of possible advantages and drawbacks of this new and unexplored theory, so to identify some guidelines for choosing parameters fundamental for the analyses and the development of models for particular structural analyses. In the first year of the PhD course, the state of the art of this theory was studied and the bond-based linear and nonlinear static solvers developed in Matlabr were analyzed, employed and improved. During the second year of PhD course, the author of this thesis has focused her attention on the second version of the theory, based on concepts of advanced mathematics. She has become familiar with it, thanks to the functional analysis course that she had attended in the first year. One of the main original contributions of the present work to the existing literature is the development of the 2D linearization of the state-based “linear peridynamic solid” model in the state-based formulation. These models are useful whenever simplifying assumptions of plane stress and plane strain can be adopted for the simulation of a system, which, otherwise, would be described by a 3D model requiring high computational resources (time and memory). Particular attention is paid to this aspect, because, being a nonlocal model, implementing a peridynamic code is, in general, more computationally expensive than a code based on a local approach. The study of the state-based version started before going abroad and the development of the 2D models was completed during the six month stay at the University of Nebraska-Lincoln in USA. Both static and dynamic codes have been developed and the relevant parameters of these models have been analyzed. These linearized models are described in chapter 1.2.2. The study of failure criteria in state-based Peridynamics and the improvement of the algorithms in Matlabr to accelerate the codes and to optimize memory resources have been the main issues of the third year research. Some failure criteria, presented in section 1.2.3, have been proposed for brittle homogeneous linear elastic materials. They are criteria based on the maximum admissible stretch: a given bond fails at a critical stretch obtained by the work required to break that bond and this work is related to the fracture energy of the material. The results are compared to experimental data both for static and for dynamic cases, in bondbased and in state-based formulations. The detailed description of the algorithms can be found in chapter 3, while the results are illustrated in chapters 4 and 5.
Nella teoria classica della meccanica dei solidi, la formulazione matematica include derivate parziali, grazie alle quali si possono rappresentare stati di deformazione come funzioni degli spostamenti relativi dei nodi in cui è discretizzato il sistema continuo. Una carenza rilevante dovuto all’utilizzo delle derivate è legato ai risultati privi di significato fisico ottenuti in prossimità delle discontinuità perché le derivate non sono definite laddove manca un campo di spostamenti continuo, come può capitare in presenza di dislocazioni, vuoti, cricche, interfacce tra fasi differenti nello stesso corpo e bordi dei grani. Dato che la formazione spontanea e la crescita di discontinuità sono di grande importanza in meccanica dei solidi, diverse tecniche sono state utilizzate per superare questa incapacità della teoria di descrivere il comportamento dei materiali in tali condizioni, perché situazioni in cui le strutture sono incapaci di continuare a svolgere la propria funzione devono essere evitate, specialmente per strutture aerospaziali, in primo luogo, per ragioni di sicurezza ed, in secondo luogo, per motivi economici. Uno di questi nuovi approcci riguarda l’utilizzo di teorie non locali basate su formulazioni integrali (più precisamente formulazioni integro-differenziali), definite anche quando campi di spostamento non derivabili sono presenti. La teoria “Peridynamics” è una di queste teorie: è stata proposta da Stewart Silling nel 2000 [1] così da adottare una formulazione unica e coerente capace di descrivere i comportamenti dei materiali in corpi sia continui che discontinui, evitando l’uso di equazioni alle derivate parziali o la definizione a priori di alcune condizioni che possono influenzare (e in un certo senso favorire) dei risultati. Ci sono due versioni di modelli peridinamici: la state-based, e un suo caso particolare, la bond-based, che è stata introdotta per prima (vedi [1, 2]). Nella versione bond-based, le forze tra due punti materiali dependono unicamente dal loro spostamento relativo e dalla loro posizione relativa iniziale, oltre che dalle proprietà del materiale. Vista la sua semplicità a confronto con la seconda versione, la maggior parte delle applicazioni e degli articoli sulla Peridynamica ha adottato la formulazione bond-based. Tuttavia, i modelli nella formulazione bond-based sono caratterizzati da alcune limitazioni (le stesse dei modelli di altre teorie atomistiche e dei modelli di dinamica molecolare [3], anche se la Peridinamica è una teoria del continuo, non discreta), la più notevole di queste è il modulo di Poisson fisso: 1/4 nelle simulazioni 3D oppure in caso di deformazione piana 2D, e 1/3 nelle simulazioni in stato di tensione piana 2D (si veda per esempio [1, 4]). Questa particolarità implica altre restrizioni, come l’impossibilità di riprodurre la condizione di incomprimibilità plastica in maniera accurata. Tuttavia, per la maggior parte degli scopi, la formulazione bond-based è sufficiente e fornisce risultati approssimati soddisfacenti. I modelli della versione state-based rimuovono queste restrizioni, permettendo che le interazioni tra due punti possano dipendere da tutte le interazioni (i “bond”) connessi ad almeno uno dei due punti, tramite delle mappe avanzate chiamate “states”. Inoltre, ci sono due tipi di formulazioni state-based: la ordinary e la non-ordinary [2, 5, 6]. Nella formulazione ordinary, le forze tra due punti materiali agiscono lungo la congiungente i due punti nella configurazione deformata, mentre nella formulazione non-ordinary, questa caratteristica non è più vera. La formulazione ordinary della state-based necessita di modelli costitutivi appositamente derivati, come per esempio i modelli di viscoelasticità e platicità in [7, 8]. Per la formulazione non-ordinary della state-based, due approcci sono stati proposti: lo sviluppo di un modello esplicito per l’espressione dello state della forza peridinamica [2] e lo sviluppo di una mappa grazie alla quale le relazioni costitutive della meccanica classica sono incorporate per stabilire indirettamente la relazione tra la forza d’interazione e la deformazione. I modelli derivanti dal secondo approccio sono chiamati modelli correspondence [2]. L’argomento di questa tesi è lo sviluppo di modelli per particolari tipi di analisi e la ricerca di possibili vantaggi e inconvenienti di questa teoria nuova ed inesplorata, così da identificare alcune linee guida per la scelta di parametri fondamentali per le analisi. Durante il primo anno del corso di dottorato, lo stato dell’arte relativo a questa teoria è stato studiato e i solutori statici lineari e non lineari nella formulazione bond-based sviluppati precedentemente in ambiente Matlabr sono stati analizzati, usati e migliorati. Durante il secondo anno, l’autrice di questa tesi si è concentrata sulla seconda versione, basata su concetti di matematica avanzata con cui ha preso dimestichezza grazie al corso di analisi funzionale seguito il primo anno. Uno dei principali contributi originali alla letteratura esistente presenti in questa tesi è lo sviluppo dei modelli linearizzati 2D del modello solido lineare nella formulazione state-based. Questi modelli sono particolarmente utili quando semplificazioni di stato piano di tensione o di deformazione possono essere assunte per la simulazione di un sistema tridimensionale, che altrimenti verrebbe descritto da un modello 3D che necessiterebbe di risorse computazionali più elevate (in termini di tempo e memoria). Una particolare attenzione è richiesta per quest’aspetto, perché, essendo un approccio non locale, implementare un codice basato sulla teoria peridinamica richiede in generale più risorse computazionali di un codice basato su un approccio locale. Lo studio della versione state-based è iniziato prima di andare all’estero e lo sviluppo dei modelli 2D si è poi completato durante il soggiorno di sei mesi alla University of Nebraska-Lincoln negli Stati Uniti. Sono stati sviluppati sia un codice dinamico che uno statico. I parametri principali di questi modelli sono stati analizzati e i modelli linearizzati si possono trovare descritti nel capitolo 1.2.2. Lo studio dei criteri di frattura adottabili nella formulazione state-based e il miglioramento degli algoritmi in Matlabr per accelerare i codici e ottimizzare le risorse di memoria e gestione dei dati sono stati gli argomenti principali del terzo anno. Alcuni criteri di frattura, presentati nel capitolo 1.2.3, sono stati proposti per materiali lineari elastici omogenei e caratterizzati da frattura fragile. Sono criteri basati sul massimo allungamento: un’interazione non locale (“bond”) viene meno quando un valore critico di allungamento è raggiunto; questo valore di allungamento critico è calcolato dal lavoro richiesto per rompere il bond e questo lavoro è a sua volta legato all’energia di frattura. I risultati ottenuti sono stati confrontati con dati sperimentali per casi sia statici che dinamici, sia nella formulazione bondbased che in quella state-based. La descrizione dettagliata degli algoritmi si trova nel capitolo 3, mentre i risultati sono riportati nei capitoli 4 e 5.

The scope of the current thesis is the investigation of the seismic behavior of complex structures of soccer stadium in the city of Adana, Turkey. The main structural parts of the building of the stadium are reinforced concrete tribunes, steel façade and cable-stayed roof, resting on the structures of the façade. The behavior of the coupled model in case of seismic excitation is studied. The coupled model is defined as a structural model that contains together all main structural parts: the tribunes, the façade and the roof. In the engineering practice, a large-span roof and supporting substructures (façade, tribunes) are differentiated and analyzed separately. In case when the seismic analysis has to be done, the separated analysis has to be performed with caution and possible amplification effect of the seismic action for the structural model with all main structural blocks introduced has to be taken into account. The amplification effect is defined as the increase of the displacements, total base shear and internal forces in the structural elements. To investigate the extent of the amplification effect, the results obtained from the analysis of coupled and uncoupled models were compared. The results obtained from the modal spectral response analysis and nonlinear dynamic analysis of different structural models show a significant amplification of the displacements of the roof structure and façade bearing columns for a coupled model, with the subsequent increase of the total base shear transferred to the substructures form the roof and internal forces in the elements. Methods of improving the structural behavior for the seismic excitation have been investigated. In particular, the effect of installation of seismic isolators for the roof structures has been studied. For the structural models with the isolated roof, the results of the analysis of both coupled and uncoupled models have been improved and all design requirements have been verified.

Thesis (Ph.D)--Civil and Environmental Engineering, Georgia Institute of Technology, 2009.
Committee Chair: Haj-Ali, Rami; Committee Member: White, Donald; Committee Member: Will, Kenneth; Committee Member: Yavari, Arash; Committee Member: Yoganathan, Ajit. Part of the SMARTech Electronic Thesis and Dissertation Collection.

The analysis procedures employed in earthquake engineering can be classified as linear static, linear dynamic, nonlinear static and nonlinear dynamic. Linear procedures are usually referred to as force controlled and require less analysis time and less computational effort. On the other hand, nonlinear procedures are referred to as deformation controlled and they are more reliable in characterizing the seismic performance of buildings. However, there is still a great deal of unknowns for nonlinear procedures, especially in modelling the reinforced concrete structures. Turkey ranks high among all countries that have suffered losses of life and property due to earthquakes over many centuries. These casualties indicate that, most regions of the country are under seismic risk of strong ground motion. In addition to this phenomenon, recent studies have demonstrated that near fault ground motions are more destructive than far-fault ones on structures and these effects can not be captured effectively by recent nonlinear static procedures. The main objective of this study is developing a simple nonlinear dynamic analysis procedure which is named as &ldquo
Dynamic Pull Analysis&rdquo
for estimating the seismic response of multi degree of freedom (MDOF) systems. The method is tested on a six-story reinforced concrete frame and a twelve-story reinforced concrete frame that are designed according to the regulations of TS-500 (2000) and TEC (1997).

This thesis presents the results of basically two separate studies. The first study involved identifying structural and earthquake parameters that influenced seismic structural collapse. The parameter study involved nonlinear dynamic analyses using single-degree-of-freedom (SDOF) bilinear models. Four parameters were associated with the SDOF models â the lateral stiffness, the post-yield stiffness ratio, the yield strength, and the stability ratio (P-Delta effects). Then, three parameters were associated with the ground motions â the records themselves, the lateral ground motion scales, and the vertical ground motion scales.

From the parameter study, it was found that the post-yield stiffness ratio augmented by P-Delta effects (rp) in conjunction with the ductility demand was the best predictor of collapse. These two quantities include all four structural parameters and the seismic displacement demands. It was also discovered in the parameter study that vertical accelerations did not significantly influence lateral displacements unless a given combination of model and earthquake parameters was altered such that the model was on the verge of collapsing.

The second study involved Incremental Dynamic Analysis (IDA) using bilinear SDOF models representative of low rise buildings in both the Western United States (WUS) and the Central and Eastern United States (CEUS). Models were created that represented three, five, seven, and nine story buildings. Five sites from both the WUS and CEUS were used. Four different damage measures were used to assess the performance of the buildings. The IDA study was primarily interested in the response of the structures between the earthquake intensities that have a 10 percent probability of occurring in 50 years (10/50) and 2 percent probability of occurring in 50 years (2/50).

The results showed that all structures could be in danger of severe damage and possible collapse, depending on which damage measure and which earthquake was used. It is important to note, though, that the aforementioned is based on a damage-based collapse rule. The damage-based rule results were highly variable.

Using an intensity-based collapse rule, proved to be more consistent. Due to the nature of the bilinear models, only those structures with negative rp values ever collapsed using an intensity-based collapse rule. Most of the WUS models had positive rp values and many of the CEUS models had negative rp values. While many of the CEUS structures had negative rp values, which made them prone to collapse, most of the CEUS structures analyzed did not collapse at the 2/50 intensity. The reason was that the periods of the CEUS models were much longer than the approximate periods that were required to determine the strengths. Consequently, the strength capacity of most of the CEUS models was much greater than the seismic strength demands. While many of the CEUS models did have sudden collapses due to the large negative rp values, the collapses happened at intensities that were generally much higher than the 2/50 event.

In the IDA, it was also shown that vertical accelerations can significantly affect the ductility demands of a model with a negative rp post-yield stiffness ratio as the earthquake intensity approaches the collapse intensity. Since IDA is concerned with establishing collapse limit states, it seems that the most accurate collapse assessments would include vertical accelerations.
Master of Science

Thesis (Ph. D.)--Ohio State University, 2005.
Title from first page of PDF file. Document formatted into pages; contains xvii, 221 p.; also includes graphics (some col.). Includes bibliographical references (p. 210-221). Available online via OhioLINK's ETD Center

Past earthquake events have shown that seismic damage to electrical power systems in commercial buildings, hospitals, and other systems such as public service facilities can cause serious economic losses as well as operational problems. A methodology for evaluation of the seismic vulnerability of electrical power systems is needed and all essential components of the system must be included. A key system component is the switchboard cabinet which houses many different elements which control and monitor electrical power usage and distribution within a building. Switchboard cabinets vary in size and complexity and are manufactured by a number of different suppliers; a typical cabinet design was chosen for detailed evaluation in this investigation. This study presents a comprehensive framework for the evaluation of the seismic performance of electrical switchboard cabinets. This framework begins with the introduction and description of the essential equipment in building electrical power systems and explains possible seismic damage to this equipment. The shortcomings of previous studies are highlighted and advanced finite element models are developed to aid in their vulnerability estimation. Unlike previous research in this area, this study proposes practical, computationally efficient, and versatile numerical models, which can capture the critical nonlinear behavior of switchboard cabinets subjected to seismic excitations. A major goal of the current study was the development of nonlinear numerical models that can accommodate various support boundary conditions ranging from fixed, elasto-plastic to free. Using both linear and nonlinear dynamic analyses, this study presents an enhanced evaluation of the seismic behavior of switchboard cabinets. First the dynamic characteristics of switchboard cabinets are determined and then their seismic performance is assessed through nonlinear time history analysis using an expanded suite of ground motions. The seismic responses and associated ground motions are described and analyzed using probabilistic seismic demand models (PSDMs). Based on the PSDMs, the effectiveness and practicality of common intensity measures are discussed for different components. Correlation of intensity measures and seismic responses are then estimated for each component, and their seismic performance and uncertainties are quantified in terms of engineering demand parameters. The results of this study are intended for use in the seismic vulnerability assessment of essential electrical equipment in order to achieve more reliable electrical power systems resulting in reduced overall risk of both physical and operational failures of this important class of nonstructural components.

The offshore industry is moving deeper and deeper into the ocean depths and a subsequent technological advancement are inevitable factors. Steel Catenary Risers (SCRs) are the most popular type of deep water risers and are very important part of any deep-water developments. Although the simplicity in installation and the associated economic advantage makes it widely popular, these highly slender structures are very sensitive to dynamic loads and fatigue. Hang-off point where the riser is connected to the floater and Touch Down Zone (TDZ) where the riser interacts with the seabed are the two-important fatigue critical regions in an SCR. Fatigue design at TDZ remains a challenging topic among riser engineers and the soil structure interaction here makes it extremely complex to design for fatigue. Linear soil structure models, which are popular among the design professionals due to its simplicity are extremely conservative and the industry is slowly moving towards the nonlinear soil models. This research investigates the effects of implementing the nonlinear soil model into the fatigue design of SCRs under randomly generated waves with detailed comparison with the linear soil model. The uncertainties related to estimation of fatigue damage at TDZ and the influence of duration of simulation are studied in detail and some significant observations and findings are presented in this research. A very extensive effort to understand the effect of different order of waves (of varying intensities) also formed a part of this study which yielded crucial results which opens new doors in this topic.

This thesis examines the seismic internal retrofitting of existing deficient reinforced concrete (RC) structures by using structural steel members. Both experimental and numerical studies were performed. The strengthening methods utilized with the scope of this work are chevron braces, internal steel frames (ISFs), X-braces and column with shear plate. For this purpose, thirteen strengthened and two as built reference one bay one story portal frame specimens having 1/3 scales were tested under constant gravity load and increasing cyclic lateral displacement excursions. In addition, two ½
scaled three bay-two story frame specimens strengthened with chevron brace and ISF were tested by employing continuous pseudo dynamic testing methods. The test results indicated that the cyclic performance of the Xbrace and column with shear plate assemblage technique were unsatisfactory. On the other hand, both chevron brace and ISF had acceptable cyclic performance and these two techniques were found to be candidate solutions for seismic retrofitting of deficient RC structures. The numerical simulations by conducting nonlinear static and dynamic analysis were used to estimate performance limits of the RC frame and steel members. Suggested strengthening approaches, chevron brace and ISF, were also employed to an existing five story case study RC building to demonstrate the performance efficiency. Finally, design approaches by using existing strengthening guidelines in Turkish Earthquake Code and ASCE/SEI 41 (2007) documents were suggested.

Dans le processus de conception des véhicules, la vibration et le bruit sont des sujets d’étude très importants. En effet, les vibrations sont susceptibles d’affecter le comportement dynamique des structures et le bruit dégrade le confort acoustique des passagers. L’objectif principal de la thèse est de proposer un ensemble de méthodes pour l’optimisation du comportement dynamique des systèmes complexes afin de réduire les vibrations des structures et le bruit dans l’habitacle. À cet effet, on s’intéresse à des stratégies de contrôle des interfaces, comme le collage de couches viscoélastiques sur les zones les plus déformées, ou l’introduction de dispositifs frottants calibrés pour ajouter de l’amortissement à certaines fréquences de résonance. Les structures assemblées résultantes sont étudiées numériquement par une méthode de synthèse modale généralisée. La méthode de synthèse modale proposée contient plusieurs niveaux de condensation. Le premier concerne les degrés de libertés (DDL) internes de chaque sous-structure. La deuxième condensation s’effectue sur les modes de branches, de sorte à réduire le nombre de DDL aux interfaces entre les sous-structures. Pour les systèmes couplés fluide/structure, une troisième condensation portant sur les DDL du fluide est proposée. Suite à ces condensations, la dimension du système est fortement réduite. Cette méthode permet alors d’obtenir aussi bien la réponse forcée de la structure que les fluctuations du champ de pression dans le fluide. Les chemins de transmission acoustiques et vibratoires peuvent également être déduits des contributions modales intermédiaires. On montre que ces paramètres modaux peuvent être utilisés comme fonctions objectif pour une démarche d’optimisation des interfaces. Le front de Pareto des conceptions optimales est obtenu avec un algorithme génétique multi-objectif élitiste, appliqué à une approximation par krigeage de la fonction objectif. Cette approche modale est étendue à l’étude de systèmes non-linéaires. L’hypothèse fondamentale est que les modes non-linéaires sont faiblement couplés. Les paramètres modaux non-linéaires (fréquences propres, amortissements...), dépendent des amplitudes modales. L’idée est alors de calculer des modes normaux non-linéaires en fonction de leur amplitude et de superposer leurs réponses pour obtenir celle de la structure. La méthode est appliquée à des systèmes incorporant des non-linéarités de type Duffing et de frottement sec. Le cas particulier du frottement sec est considéré à travers un modèle de Masing généralisé. Deux approches modales sont développées : l’une basée sur les modes complexes, et l’autre basée sur les modes réels. L’utilisation de modes complexes ou réels dans la synthèse modale conduit à des termes d’amortissement par frottement différents. On montre que la synthèse modale non-linéaire combinée au modèle de Masing généralisé aboutit à une méthode numérique simple, rapide et efficace pour décrire le comportement non-linéaire de structures soumise à du frottement sec
Noise and vibration are important topics in the automotive industry for several reasons, including passenger comfort and structural integrity. The main objective of this thesis is to propose a series of appropriate methods to optimize structural system characteristics, so that the vibration and noise can be reduced. To achieve this goal, interface control strategies are employed, including bonding viscoelastic layers onto the most heavily deformed zones and introducing frictional damping devices calibrated on certain resonance frequencies. Such built-up structural systems are numerically investigated via a generalized modal synthesis approach that incorporates several groups of modes. The employed modal synthesis approach consists of several levels of condensation. The first one is on the internal degrees of freedoms (DOFs) of each substructure, and the second condensation is on the branch modes so as to reduce the boundary DOFs among substructures. For coupled fluid-structural systems, a third condensation on the fluid DOFs is suggested. With these condensation techniques, the system dimension can be significantly reduced. The method allows us to obtain the forced response of the structures as well as the pressure variation of the fluids. Additionally, modal parameters characterizing vibration and noise transmission paths can be deduced as mid-stage results. We show that these modal parameters can be used as optimization objective during the interface configuration design. The Pareto front of the optimal design is achieved by employing Kriging approximations followed with an elitist multi-objective genetic algorithm. Another advantage of the modal approach is that a modal overview on the system characteristics is provided by analyzing the natural frequencies, modal damping ratios and the aforementioned modal parameters. The modal synthesis approach is further extended to study nonlinear systems. The basic assumption is that the nonlinear modes are weakly coupled. Nonlinear modal parameters, such as modal frequency and modal damping ratio, contain the essential nonlinear information and depend on modal amplitude. The main idea is to compute nonlinear normal modes according to their modal amplitude and superimpose the response of several nonlinear modes to obtain the overall forced response. The method is applied to systems involving Duffing and dry friction nonlinearities. In the case of dry friction, a generalized Masing model is considered to capture the dry friction nature. Both complex modes and real modes are used in the modal synthesis, leading to different frictional damping terms. We show that the nonlinear modal synthesis combined with the generalized Masing model yields a simple, fast and efficient numerical method to describe nonlinear performance of structures with dry friction

The rapid growth of high-rise high-density urban areas in coastal and near coastal, hurricane-prone cities has been observed globally and in the United States in recent decades. Favored by modern urban growth and planning policies, this trend is expected to accelerate in future. Recent climate change studies suggest a significant increase in the destructiveness of hurricanes in past 30 years by both increases in lifetime and intensity of hurricanes. Current prescriptive wind design approach does not provide transparent methods and criteria to reliably quantify the performance of buildings as well as the functional requirements necessary to accommodate large populations during extreme wind. Since this approach primarily intends to keep the structural system essentially elastic, the more efficient design may be achievable by allowing controlled inelasticity in structural components. All these facts put a great emphasis on using a reliable wind design and assessment approach evidently describing the performance of high-rise building to wind loads beyond the current design wind loads. This dissertation presents the development of a wind performance-based engineering approach and its practical implementation for three, 47-, 40- and 30-story steel moment frame high-rise buildings. In this study, the nonlinear dynamic responses of the buildings to different wind hazard levels were evaluated by developing 3D nonlinear finite element models and utilizing a wind incremental dynamic analysis (IDA) approach. The wind loading for the 47-story building was measured by conducting wind pressure testing on a scaled rigid model at the Wall of Wind (WOW) facility at Florida International University. For two other buildings wind loads were acquired using TPU Aerodynamic Database. Using the IDA results and adopting available wind performance criteria, a wind performance assessment approach was developed representing the estimated performance levels as a function of the basic wind speed. Three types of wind performance were evaluated: structural component performance; cladding performance to wind-induced shear deformation; and serviceability motion comfort performance. This evaluation indicated remarkable lateral capacity associated with allowing controlled structural nonlinearity, in contrast to considerations required to assure acceptable serviceability and non-structural (e.g. cladding) performances.

This dissertation discusses the potential for using a conventional main lateral-force resisting system, combined with the reserve strength in the gravity framing, and or auxiliary collapse-inhibiting mechanisms deployed throughout the building, or enhanced shear tab connections, to provide adequate serviceability performance and collapse safety for seismic and wind hazards in the central and eastern United States. While the proposed concept is likely applicable to building structures of all materials, the focus of this study is on structural steel-frame buildings using either non-ductile moment frames with fully-restrained flange welded connections not specifically detailed for seismic resistance, or ductile moment frames with reduced beam section connections designed for moderate seismic demands. The research shows that collapse prevention systems were effective at reducing the conditional probability of seismic collapse during Maximum Considered Earthquake (MCE) level ground motions, and at lowering the seismic and wind collapse risk of a building with moment frames not specifically detailed for seismic resistance. Reserve lateral strength in gravity framing, including the shear tab connections was a significant factor. The pattern of collapse prevention component failure depended on the type of loading, archetype building, and type of collapse prevention system, but most story collapse mechanisms formed in the lower stories of the building. Collapse prevention devices usually did not change the story failure mechanism of the building. Collapse prevention systems with energy dissipation devices contributed to a significant reduction in both repair cost and downtime. Resilience contour plots showed that reserve lateral strength in the gravity framing was effective at reducing recovery time, but less effective at reducing the associated economic losses. A conventional lateral force resisting system or a collapse prevention system with a highly ductile moment frame would be required for regions of higher seismicity or exposed to high hurricane wind speeds, but buildings with collapse prevention systems were adequate for many regions in the central and eastern United States.
Ph. D.

La surveillance de la réponse structurale est fondamentale pour estimer la performance des bâtiments et réduire les pertes lors de futurs séismes. Un moyen pratique de détecter les changements de comportement structural consiste à analyser les variations des propriétés élastiques lors d'excitations dynamiques. Dans ce travail, on montre que les variations de la fréquence fondamentale des bâtiments lors de tremblements de terre (faibles à forts) pourraient être expliquées par des processus élastiques non linéaires qui se produisent à l'intérieur du matériau, et qui finalement affectent le comportement macroscopique global des bâtiments. Ces processus élastiques non linéaires sont responsables de la diminution temporaire ou permanente de la rigidité structurale, pouvant expliquer les processus de récupération des propriétés élastiques observés à la suite d'événements sismiques. Cette étude comble le fossé entre des expériences de laboratoire à l'échelle microscopique et des observations sismologiques à l'échelle macroscopique, où l’élasticité non linéaire est également observée. Dans un premier temps, une base de données sismiques établie dans le cadre de cette thèse est présentée, incluant des réponses de bâtiments instrumentés de façon permanente dans le monde: des milliers d’enregistrements de mouvements sismiques et plusieurs bâtiments du Japon et des États-Unis ont été traités, apportant des connaissances utiles pour le domaine du génie parasismique, notamment pour la prédiction empirique de la réponse structurale en fonction de mesures d'intensité du mouvement au sol. Les incertitudes associées à la prédiction d’endommagement sont présentées, ainsi que l'évaluation de la vulnérabilité d'un bâtiment sous forme de courbes de fragilité. Ensuite, la base de données est utilisée pour analyser les signatures élastiques non linéaires dans les bâtiments, en particulier les effets de la dynamique lente (ou relaxation). Les variations des fréquences de résonance sont étudiées à court et à long terme, en estimant la contribution du sol à la réponse du système sol-structure. Différents états structuraux sont déduits en fonction des amplitudes de chargement et propriétés observées via les enregistrements. Des modèles de relaxation développés en laboratoire sont ensuite adaptés aux données des bâtiments afin de caractériser la densité de fissuration et les hétérogénéités, en effectuant des comparaisons entre les états structuraux avant et après de fortes excitations telles que le séisme de 2011 (Mw=9) de Tohoku (Japon). Les effets des chargements sont observés lors de la récupération des séquences de répliques. Les résultats sont étendus à différentes typologies de bâtiments, en analysant l'influence du matériau et des caractéristiques de chargement, notamment les taux de déformation. Enfin, quelques conclusions générales sont présentées, ainsi qu'une perspective de travail utilisant des outils de machine learning pour prédire la réponse de bâtiments en fonction de signatures élastiques non linéaires observées
Monitoring structural response is fundamental for evaluating the performance of buildings and reducing losses during future earthquakes. One practical way to detect changes in structural behavior is analyzing variations of elastic properties during dynamic excitations. Here we show that variations in the fundamental frequency of buildings during (weak -to- strong) earthquakes might be explained by nonlinear elastic processes carried out within the structural material, which affect the global macroscopic structural behavior. These nonlinear elastic processes are responsible for both transitory and permanent structural softening, and might explain the intriguing recovery effects observed in the fundamental frequency of buildings following seismic events. This study bridges the gap between microscale laboratory experiments and macroscale seismological observations, where nonlinear elasticity is also observed. In the first part of this study, a new seismic database of building responses is presented: thousands strong motion recordings and several buildings from Japan and US were processed, providing useful tools for the earthquake engineering community, notably for the empirical prediction of structural response as a function of several ground motion intensity measures. Examples of uncertainties associated to damage prediction are presented, as well as the vulnerability assessment of a building throughout fragility curves. Next, the seismic database is used to analyze nonlinear elastic signatures in buildings, particularly the slow dynamics or relaxation effects. Variations of resonant frequencies are monitored at both short and long-term, estimating the contribution of soil in the response of the system soil-structure. Different levels of damage are inferred according to loading amplitudes and structural states. Some laboratory-based models of relaxation are adapted to the building data in order to infer crack-density and heterogeneities over time, making comparisons between structural states before and after large excitations such as the Mw 9 Tohoku earthquake. Conditioning effects are observed during the backbone recovery of aftershocks sequences. The results are extended to different building typologies, analyzing the influence of structural material and loading features, notably strain-rates. Finally, some general conclusions are presented, together with a perspective work using machine learning to predict building response based on nonlinear elastic signatures

In this thesis consideration is given to a selection of nonlinear dynamic problems in the field of offshore engineering. Hydrodynamic loading on fixed horizontal and vertical tubular members and the dynamic response of articulated towers together with the distribution of shear force and bending moment along the tower are investigated using various wave theories. Effects of nonlinear convective acceleration terms in the calculation of fluid inertia forces and moments are examined and attention is given to integration of wave forces up to the free surface for vertical members. Calculation of fluid loading at the displaced position of the articulated tower and any Mathieu type instabilities that may occur have been considered. The dynamic analysis of a damaged Single Anchor Leg Storage (SALS) system subject to loss of buoyancy in the yoke chamber is studied. The equations of motion of the yoke/riser system are derived assuming large displacements and solved in the time domain. Time histories of the response, variations of the riser tension, velocities of riser top end and the time histories of pivot reactions are given. Natural periods and mode shapes for small displacements of the system are calculated. Two methods of simulating random seas, both represented by a sum of harmonic wave components, are used to simulate second order low frequency (slow drift) force on a tanker in head seas by Pinkster's time domain method. In one method the wave amplitudes are generated randomly from a Rayleigh distribution and in the other they are obtained deterministically via the wave spectrum. Time histories of slow drift force and response together with simulation results with various duration lengths are presented and compared. Estimates of the extreme vessel response and its relation to rms value are compared with the result of a commonly used method of determining peak/rms ratios. The results of these investigations highlight the importance of accurately simulating nonlinear effects in both fixed, floating and compliant offshore structures from the point of view of safe design and operation of such- systems.

The nonlinear dynamic analysis to obtain the response of whole building structures or structural components under blast loading can be computationally prohibitive. Two approaches have been considered in this study to improve the efficiency of such analyses: i) to employ an appropriate time integration scheme and, ii) to employ accurate simplified models of structural components. A new implicit-explicit time integration scheme has been developed and implemented with a novel automatic element-based mesh partitioning approach. The scheme allows simultaneous execution of implicit integration and explicit integration in different parts of a system to maximise computational efficiency. The developed scheme has also been notably incorporated to the novel domain decomposition approach developed previously at Imperial College London. The scheme is also successfully incorporated with the mixed-dimensional coupling technique included in the domain decomposition approach. Simplified models of structural components have been improved for a better representation of responses under blast loading. Mechanical models of fin plate connections have been modified by including material nonlinearity and material strain rate effect in the coupled axial and shear response of bolt rows. The flat shell elements have been verified in their ability to capture the influence of transverse damage in floor slabs due to uplift on the in-plane diaphragm stiffness and strength. These simplified models have been incorporated in the global model of a reference building, which has been analysed and assessed under characteristic blast loading. Typical masonry cavity cladding has been investigated as a case study. The failure mode and the interaction between the cladding and the structural frame have been successfully obtained from mesoscale models employing the mixed-dimensional domain decomposition approach and the implicit-explicit time integration scheme. A SDOF model based on the results of the detailed model has been constructed and incorporated in the global model of the reference building.

The response of a nonlinear dynamic structure can be sensitive to its initial conditions or parameters. In order to ensure its safety and robustness, an understanding of the global structural responses is necessary. This requires performing a parameter study. However, this is extremely difficult due to the complexity arising from nonlinearities and the associated computational costs. Hence, it is highly desirable to have new methods to tackle these difficulties.

[EN] The test for determining the resonance frequencies has traditionally been used to investigate the mechanical integrity of concrete cores, to assess the conformity of concrete constituents in different accelerated durability tests, and to ascertain constitutive properties such as the elastic modulus and the damping factor. This nondestructive technique has been quite appealed for evaluation of mechanical properties in all kinds of durability tests. The damage evolution is commonly assessed from the reduction of dynamic modulus which is produced as a result of any cracking process. However, the mechanical behavior of concrete is intrinsically nonlinear and hysteretic. As a result of a hysteretic stress-strain behavior, the elastic modulus is a function of the strain. In dynamic tests, the nonlinearity of the material is manifested by a decrease of the resonance frequencies, which is inversely proportional to the excitation amplitude. This phenomenon is commonly referred as fast dynamic effect. Once the dynamic excitation ceases, the material undergoes a relaxation process whereby the elastic modulus is restored to that at rest. This phenomenon is termed as slow dynamics. These phenomena (fast and slow dynamics) find their origin in the internal friction of the material. Therefore, in cement-based materials, the presence of microcracks and interfaces between its constituents plays an important role in the material nonlinearity. In the context of the assessment of concrete durability, the damage evolution is based on the increase of hysteresis, as a result of any cracking process. In this thesis three different nondestructive techniques are investigated, which use impacts for exciting the resonant frequencies. The first technique consists in determining the resonance frequencies over a range of impact forces. The technique is termed Nonlinear Impact Resonant Acoustic Spectroscopy (NIRAS). It consists in ascertaining the downward resonant frequency shift that the material undergoes upon increasing excitation amplitude. The second technique consists in investigating the nonlinear behavior by analyzing the signal corresponding to a single impact. This is, to determine the instantaneous frequency, amplitude and attenuation variations corresponding to a single impact event. This technique is termed as Nonlinear Resonant Acoustic Single Impact Spectroscopy (NSIRAS). Two techniques are proposed to extract the nonlinear behavior by analyzing the instantaneous frequency variations and attenuation over the signal ring down. The first technique consists in discretizing the frequency variation with time through a Short-Time Fourier Transform (STFT) based analysis. The second technique consists of a least-squares fit of the vibration signals to a model that considers the frequency and attenuation variations over time. The third technique used in this thesis can be used for on-site evaluation of structures. The technique is based on the Dynamic Acousto- Elastic Test (DAET). The variations of elastic modulus as derived through NIRAS and NSIRAS techniques provide an average behavior and do not allow derivation of the elastic modulus variations over one vibration cycle. Currently, DAET technique is the only one capable to investigate the entire range of nonlinear phenomena in the material. Moreover, unlike other DAET approaches, this study uses a continuous wave source as probe. The use of a continuous wave allows investigation of the relative variations of the elastic modulus, as produced by an impact. Moreover, the experimental configuration allows one-sided inspection.
[ES] El ensayo de determinación de las frecuencias de resonancia ha sido tradicionalmente empleado para determinar la integridad mecánica de testigos de hormigón, en la evaluación de la conformidad de mezclas de hormigón en diversos ensayos de durabilidad, y en la terminación de propiedades constitutivas como son el módulo elástico y el factor de amortiguamiento. Esta técnica no destructiva ha sido ampliamente apelada para la evaluación de las propiedades mecánicas en todo tipo de ensayos de durabilidad. La evolución del daño es comúnmente evaluada a partir de la reducción del módulo dinámico, producido como resultado de cualquier proceso de fisuración. Sin embargo, el comportamiento mecánico del hormigón es intrínsecamente no lineal y presenta histéresis. Como resultado de un comportamiento tensión-deformación con histéresis, el módulo elástico depende de la deformación. En ensayos dinámicos, la no linealidad del material se manifiesta por una disminución de las frecuencias de resonancia, la cual es inversamente proporcional a la amplitud de excitación. Este fenómeno es normalmente denominado como dinámica rápida. Una vez la excitación cesa, el material experimenta un proceso de relajación por el cual, el módulo elástico es restaurado a aquel en situación de reposo. Este fenómeno es denominado como dinámica lenta. Estos fenómenos ¿dinámicas rápida y lenta¿ encuentran su origen en la fricción interna del material. Por tanto, en materiales basados en cemento, la presencia de microfisuras y las interfaces entre sus constituyentes juegan un rol importante en la no linealidad mecánica del material. En el contexto de evaluación de la durabilidad del hormigón, la evolución del daño está basada en el incremento de histéresis, como resultado de cualquier proceso de fisuración. En esta tesis se investigan tres técnicas diferentes las cuales utilizan el impacto como medio de excitación de las frecuencias de resonancia. La primera técnica consiste en determinar las frecuencias de resonancia a diferentes energías de impacto. La técnica es denominada en inglés: Nonlinear Impact Resonant Acoustic Spectroscopy (NIRAS). Ésta consiste en relacionar el detrimento que el material experimenta en sus frecuencias de resonancia, con el aumento de la amplitud de la excitación. La segunda técnica consiste en investigar el comportamiento no lineal mediante el análisis de la señal correspondiente a un solo impacto. Ésta consiste en determinar las propiedades instantáneas de frecuencia, atenuación y amplitud. Esta técnica se denomina, en inglés, Nonlinear Single Impact Resonant Acoustic Spectroscopy (NSIRAS). Se proponen dos técnicas de extracción del comportamiento no lineal mediante el análisis de las variaciones instantáneas de frecuencia y atenuación. La primera técnica consiste en la discretización de la variación de la frecuencia con el tiempo, mediante un análisis basado en Short-Time Fourier Transform (STFT). La segunda técnica consiste en un ajuste por mínimos cuadrados de las señales de vibración a un modelo que considera las variaciones de frecuencia y atenuación con el tiempo. La tercera técnica empleada en esta tesis puede ser empleada para la evaluación de estructuras in situ. La técnica se trata de un ensayo acusto-elástico en régimen dinámico. En inglés Dynamic Acousto-Elastic Test (DAET). Las variaciones del módulo elástico obtenidas mediante los métodos NIRAS y NSIRAS proporcionan un comportamiento promedio y no permiten derivar las variaciones del módulo elástico en un solo ciclo de vibración. Actualmente, la técnica DAET es la única que permite investigar todo el rango de fenómenos no lineales en el material. Por otra parte, a diferencia de otras técnicas DAET, en este estudio se emplea como contraste una onda continua. El uso de una onda continua permite investigar las variaciones relativas del módulo elástico, para una señal transito
[CAT] L'assaig de determinació de les freqüències de ressonància ha sigut tradicionalment empleat per a determinar la integritat mecànica de testimonis de formigó, en l'avaluació de la conformitat de mescles de formigó en diversos assajos de durabilitat, i en la terminació de propietats constitutives com són el mòdul elàstic i el factor d'amortiment. Esta tècnica no destructiva ha sigut àmpliament apel·lada per a l'avaluació de les propietats mecàniques en tot tipus d'assajos de durabilitat. L'evolució del dany és comunament avaluada a partir de la reducció del mòdul dinàmic, produït com resultat de qualsevol procés de fisuración. No obstant això, el comportament mecànic del formigó és intrínsecament no lineal i presenta histèresi. Com resultat d'un comportament tensió-deformació amb histèresi, el mòdul elàstic depén de la deformació. En assajos dinàmics, la no linealitat del material es manifesta per una disminució de les freqüències de ressonància, la qual és inversament proporcional a l'amplitud d'excitació. Este fenomen és normalment denominat com a dinàmica ràpida. Una vegada l'excitació cessa, el material experimenta un procés de relaxació pel qual, el mòdul elàstic és restaurat a aquell en situació de repòs. Este fenomen és denominat com a dinàmica lenta. Estos fenòmens --dinámicas ràpida i lenta troben el seu origen en la fricció interna del material. Per tant, en materials basats en ciment, la presència de microfissures i les interfícies entre els seus constituents juguen un rol important en la no linealitat mecànica del material. En el context d'avaluació de la durabilitat del formigó, l'evolució del dany està basada en l'increment d'histèresi, com resultat de qualsevol procés de fisuración. En esta tesi s'investiguen tres tècniques diferents les quals utilitzen l'impacte com a mitjà d'excitació de les freqüències de ressonància. La primera tècnica consistix a determinar les freqüències de ressonància a diferents energies d'impacte. La tècnica és denominada en anglés: Nonlinear Impact Resonant Acoustic Spectroscopy (NIRAS). Esta consistix a relacionar el detriment que el material experimenta en les seues freqüències de ressonància, amb l'augment de l'amplitud de l'excitació. La segona tècnica consistix a investigar el comportament no lineal per mitjà de l'anàlisi del senyal corresponent a un sol impacte. Esta consistix a determinar les propietats instantànies de freqüència, atenuació i amplitud. Esta tècnica es denomina, en anglés, Nonlinear Single Impact Resonant Acoustic Spectroscopy (NSIRAS). Es proposen dos tècniques d'extracció del comportament no lineal per mitjà de l'anàlisi de les variacions instantànies de freqüència i atenuació. La primera tècnica consistix en la discretización de la variació de la freqüència amb el temps, per mitjà d'una anàlisi basat en Short-Time Fourier Transform (STFT). La segona tècnica consistix en un ajust per mínims quadrats dels senyals de vibració a un model que considera les variacions de freqüència i atenuació amb el temps. La tercera tècnica empleada en esta tesi pot ser empleada per a l'avaluació d'estructures in situ. La tècnica es tracta d'un assaig acusto-elástico en règim dinàmic. En anglés Dynamic Acousto-Elastic Test (DAET). Les variacions del mòdul elàstic obtingudes per mitjà dels mètodes NIRAS i NSIRAS proporcionen un comportament mitjà i no permeten derivar les variacions del mòdul elàstic en un sol cicle de vibració. Actualment, la tècnica DAET és l'única que permet investigar tot el rang de fenòmens no lineals en el material. D'altra banda, a diferència d'altres tècniques DAET, en este estudi s'empra com contrast una ona contínua. L'ús d'una ona contínua permet investigar les variacions relatives del mòdul elàstic, per a un senyal transitori. A més, permet la inspecció d'elements per mitjà de l'accés per una sola cara.
Eiras Fernández, JN. (2016). Studies on nonlinear mechanical wave behavior to characterize cement based materials and its durability [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/71439
TESIS
Premiado

The signal structure is a partial structure representation for dynamic systems. It characterizes the causal relationship between manifest variables and is depicted in a weighted graph, where the weights are dynamic operators. Earlier work has defined signal structure for linear time-invariant systems through dynamical structure function. This thesis focuses on the search for the signal structure of nonlinear systems and proves that the signal structure reduces to the linear definition when the systems are linear. Specifically, this work: (1) Defines the complete computational structure for nonlinear systems. (2) Provides a process to find the complete computational structure given a state space model. (3) Defines the signal structure for dynamic systems in general. (4) Provides a process to find the signal structure for a class of dynamic systems from their complete computational structure.

This work is motivated by the need for a numerically stable dynamic contact algorithm, for use with finite element (FE) analysis including both material and geometric nonlinearities, which imposes the appropriate full kinematic compatibility between the interfaces of impacting boundaries during a persistent dynamic contact. Several methods were previously developed based on Lagrangian multipliers or penalty functions in an attempt to impose the impenetrability condition of dynamic contact analysis. Some of these existing algorithms suffer from lack of numerical stability, and most of them are incapable of accurately predicting the persistent contact force, hence they would not be suitable for frictional dynamic contact analysis. The numerical stability and energy conservation characteristics of conventional frictionless dynamic contact algorithms using Lagrangian displacement constraints and penalty functions are investigated in this thesis. Two energy controlling dynamic contact algorithms are proposed in conjunction with the well-known Newmark trapezoidal rule, namely, regularised penalty method and Lagrangian velocity constraint. Although energy consistent, the state of the art for these two methods is somewhat similar to the conventional displacement constraints in the sense that acceleration compatibility is not imposed when simulating problems featuring persistent dynamic contact. In this work, a novel and superior energy controlling-algorithm is proposed which overcomes the aforementioned shortcomings. The proposed DVA method enforces the displacement, velocity and acceleration compatibilities (referred to as DVA constraint in this work) between the impacting interfaces, which in contrast to existing algorithms can be used for FE analysis of problems exhibiting geometric and material nonlinearities. The advanced DVA method is devised such that the kinematic compatibilities at the interface are consistent with the solution for a continuous system without any special treatment in the time-integration or solution procedure of the penetrating interface boundaries. Furthermore, this can be achieved in conjunction with all of the prevalent implicit time-integration schemes such as the trapezoidal rule, midpoint rule, HHT-α and the most recently developed Energy-Momentum family of Methods. Finally, utilising the proposed dynamic contact algorithms, a novel multi-constraints node-to-surface dynamic contact element is formulated and programmed within a geometric and material nonlinear dynamic FE analysis software. Several verification examples of frictionless mechanical contact are presented to demonstrate the superiority and performance of the developed node-to-surface contact element in conjunction with the proposed DVA constraint as well as the Lagrangian velocity constraint, providing a robust and accurate solution procedure for highly nonlinear dynamic contact analysis.

This thesis presents the results of an investigation of a multiple degree of freedom (MDOF) structure with hyperelastic bracing using nonlinear and incremental dynamic analysis. New analytical software is implemented in the investigation of the structure, and the study seeks to investigate the effectiveness of hyperelastic bracing as a seismic protection device. Hyperelastic braces incorporate a new idea of a nonlinear elastic material that gains stiffness as the brace deforms. Structural behaviors of particular concern for an MDOF frame are stability, residual displacement, base shear, and dispersion. The structure is analyzed under two ground motion records of varying content, and for two separate P-Delta cases of varying severity. Two sets of hyperelastic braces are investigated for their influence under the two ground motions and two P-Delta cases. Each scenario is analyzed using nonlinear dynamic analyses to investigate the response histories, and Incremental Dynamic Analysis (IDA) to investigate dispersion and the behavior of specific response measures as ground motion intensity increases. IDA curves are created for interstory drift and base shear for comparison between the two response measures. The research shows that the inclusion of hyperelastic braces in the MDOF frame improves the overall stability of the structure and reduces the amount of dispersion and residual displacement. The hyperelastic braces are shown to give positive performance characteristics while not detrimentally increasing system forces under regular service loads. The results highlight the benefit of the unique stiffening properties of hyperelastic braces as a seismic protection device.
Master of Science

Ce travail détaille une approche de calcul pour la résolution de problèmes dynamiques qui combinent des discrétisations en temps et dans le domaine de Laplace reposant sur une technique de sous-structuration. En particulier, la méthode développée cherche à remplir le besoin industriel de réaliser des calculs dynamiques tridimensionnels pour le risque sismique en prenant en compte des effets non-linéaires d'interaction sol-structure (ISS). Deux sous-domaines sont considérés dans ce problème. D'une part, le domaine de sol linéaire et non-borné qui est modélisé par une impédance de bord discrétisée dans le domaine de Laplace au moyen d'une méthode d'éléments de frontière ; et, de l'autre part, la superstructure qui fait référence pas seulement à la structure et sa fondation mais aussi, éventuellement, à une partie du sol présentant un comportement non-linéaire. Ce dernier sous-domaine est formulé dans le domaine temporel et discrétisé avec la méthode des éléments finis (FE). Dans ce cadre, les forces liées à l'ISS s'écrivent sous la forme d'une intégrale de convolution en temps dont le noyau est la transformée de Laplace inverse de la matrice d'impédance de sol. Pour pouvoir évaluer cette convolution dans le domaine temporel à partir d'une impédance de sol définie dans le domaine de Laplace, une approche basée sur des Quadratures de Convolution (QC) est présentée : la méthode hybride Laplace-Temps (L-T). La stabilité numérique de son couplage avec un schéma d'intégration de type Newmark est ensuite étudiée sur plusieurs modèles d'ISS en dynamique linéaire et non-linéaire. Finalement, la méthode L-T est testée sur un modèle numérique plus complexe, proche d'une application sismique de caractère industriel, et des résultats satisfaisants sont obtenus par rapport aux solutions de référence
The present work addresses a computational methodology to solve dynamic problems coupling time and Laplace domain discretizations within a domain decomposition approach. In particular, the proposed methodology aims at meeting the industrial need of performing more accurate seismic risk assessments by accounting for three-dimensional dynamic soil-structure interaction (DSSI) in nonlinear analysis. Two subdomains are considered in this problem. On the one hand, the linear and unbounded domain of soil which is modelled by an impedance operator computed in the Laplace domain using a Boundary Element (BE) method; and, on the other hand, the superstructure which refers not only to the structure and its foundations but also to a region of soil that possibly exhibits nonlinear behaviour. The latter subdomain is formulated in the time domain and discretized using a Finite Element (FE) method. In this framework, the DSSI forces are expressed as a time convolution integral whose kernel is the inverse Laplace transform of the soil impedance matrix. In order to evaluate this convolution in the time domain by means of the soil impedance matrix (available in the Laplace domain), a Convolution Quadrature-based approach called the Hybrid Laplace-Time domain Approach (HLTA), is thus introduced. Its numerical stability when coupled to Newmark time integration schemes is subsequently investigated through several numerical examples of DSSI applications in linear and nonlinear analyses. The HLTA is finally tested on a more complex numerical model, closer to that of an industrial seismic application, and good results are obtained when compared to the reference solutions

The present work addresses a computational methodology to solve dynamic problems coupling time and Laplace domain discretizations within a domain decomposition approach. In particular, the proposed methodology aims at meeting the industrial need of performing more accurate seismic risk assessments by accounting for three-dimensional dynamic soil-structure interaction (DSSI) in nonlinear analysis. Two subdomains are considered in this problem. On the one hand, the linear and unbounded domain of soil which is modelled by an impedance operator computed in the Laplace domain using a Boundary Element (BE) method; and, on the other hand, the superstructure which refers not only to the structure and its foundations but also to a region of soil that possibly exhibits nonlinear behaviour. The latter subdomain is formulated in the time domain and discretized using a Finite Element (FE) method. In this framework, the DSSI forces are expressed as a time convolution integral whose kernel is the inverse Laplace transform of the soil impedance matrix. In order to evaluate this convolution in the time domain by means of the soil impedance matrix (available in the Laplace domain), a Convolution Quadrature-based approach called the Hybrid Laplace-Time domain Approach (HLTA), is thus introduced. Its numerical stability when coupled to Newmark time integration schemes is subsequently investigated through several numerical examples of DSSI applications in linear and nonlinear analyses. The HLTA is finally tested on a more complex numerical model, closer to that of an industrial seismic application, and good results are obtained when compared to the reference solutions.

In this dissertation, a continuum sensitivity method is developed for efficient and accurate computation of design derivatives for nonlinear aeroelastic structures subject to transient
aerodynamic loads. The continuum sensitivity equations (CSE) are a set of linear partial
differential equations (PDEs) obtained by differentiating the original governing equations of
the physical system. The linear CSEs may be solved by using the same numerical method
used for the original analysis problem. The material (total) derivative, the local (partial)
derivative, and their relationship is introduced for shape sensitivity analysis. The CSEs are
often posed in terms of local derivatives (local form) for fluid applications and in terms of total
derivatives (total form) for structural applications. The local form CSE avoids computing
mesh sensitivity throughout the domain, as required by discrete analytic sensitivity methods.
The application of local form CSEs to built-up structures is investigated. The difficulty
of implementing local form CSEs for built-up structures due to the discontinuity of local
sensitivity variables is pointed out and a special treatment is introduced. The application
of the local form and the total form CSE methods to aeroelastic problems are compared.
Their advantages and disadvantages are discussed, based on their derivations, efficiency,
and accuracy. Under certain conditions, the total form continuum method is shown to be
equivalent to the analytic discrete method, after discretization, for systems governed by a
general second-order PDE. The advantage of the continuum sensitivity method is that less
information of the source code of the analysis solver is required. Verification examples are
solved for shape sensitivity of elastic, fluid and aeroelastic problems.
Ph. D.