Dissertations / Theses on the topic 'Stiffened structures'

Top-hat stiffened plates provide an effcient structure for engineering applications. During service debonding between the stiffener and the plate is a common failure mechanism. Therefore, an extensive understanding of the residual strength is required to rapidly and effciently determine precautions to be taken to ensure the safety of the structure. Critical assessment of necessary repairs reduces the through life costs and in design damage assessment can lead to optimisation through tolerance of common damage incidents. Research on damaged stiffened structures to date is primarily focused on airframe applications and considers open sections with co-cured stiffeners which are not typical of marine structures. These studies have shown that debond size and location have a significant effect on the damage mode of the panel. However, they do not consider the interaction of failure modes or ultimate failure. Typical marine composite joints are manufactured by post-curing sub-components using a chopped strand mat layer at the interface. To predict failure of these joints requires accurate assessment of the material and fracture properties and a consistent set of data which is lacking in the literature. Therefore, the research in this thesis considers the damage tolerance of top-hat stiened panels containing a debond between the stiffener and plate through numerical and experimental work. The focus of the work is post-cured top-hat multi-stiffened panels used in large marine applications manufactured from heavy weight glass vinylester woven roving. An automated tool using non-linear finite element analysis capable of modelling debond damage and assessing the ultimate and the residual strength of the panel is verified. A parametric study investigating panel topology, damage parameters and stiener type show the complexities of the damage case. Results show that top-hat stiffened panels exhibit a trend between ultimate strength and the debond size with crack initiation not necessarily propagating as geometric imperfections accelerate buckling but can provide an arrest point for crack propagation. Nominal lateral pressures are shown to significantly increase the damage tolerance. Full characterisation of typical materials is conducted experimentally providing a complete data set of mechanical characterisation and fracture data for both co-cured interfaces, typical of mid-laminate debonds and sub-component joints. Tensile, compressive, shear and exural tests are conducted and a model for the non-linearity of the woven roving in tension and shear is proposed. The fracture results show the post-cured joint exhibits a 20% increase in mode I and II strain energy release rates. The experimental data is used in a number of studies to further verify and optimise the finite element model. Mode I and II tests are simulated to ascertain the cohesive element interface strengths and Turon's interface parameters. The material data is shown to give accurate results for the structural response, crack initation and debonding of an as built large scale top-hat stiffened panel which is tested experimentally under four point bend. Therefore, the effect of skin-stiffener debonding has been investigated for top-hat stffiened panels, providing improved characterisation of the material and interfaces and guidance on the damage tolerance to damage and design parameters.

Composite stiffened panels have been extensively used in primary aerospace applications, due to their efficient stiffness/weight ratio and the ability to tailor properties. Despite their apparent superiority to metals, the susceptibility of composites to damage has proved to be a critical factor. A common example in practice is the barely visible impact damage caused by a low velocity impact event. Such events can generate inter-laminar defects (delaminations), which under compressive loading can reduce the strength and stability of the structure. There is a need to establish the influence of such damage on composite stiffened structures. Current practice allows for delamination induced strength reduction by applying strain limits to the material that ensure delamination does not produce failure before uhimate levels of loading. However, these limits are established via coupon tests, which focus on the scale of the delamination only and do not account for the interaction at the structural scale.

The thesis starts off with an introductory chapter on composite materials. This includes a definition of composites, a brief history of composite materials, their use in aerostructures (primarily as stiffened structures), and also optimization of composite structures. A literature review is then presented on postbuckling stiffened structures. This includes both experimental investigations on stiffened composite panels and investigations into secondary instabilities and mode jumping as well as their numerical modelling. Next, the Finite Element (FE) modelling of posthuckling stiffened structures is discussed, relating how ABAQUS models are set up in order to trace stiffened composite panels' buckling and postbuckling responses. An experimental programme conducted on an I-stiffened panel is described, where the panel was tested in compression until collapse. The buckling and postbuckling characteristics of the panel are presented, and then an FE model is described together with its predicted numerical behaviour of the panel's buckling and postbuckling characteristics. Focus then shifts to the modelling of failure in composites, in particular delamination failure. A literature review is conducted, looking at the use of both the Virtual Crack Closure Technique (VCCT) and interface elements in delamination modelling. Two stiffener runout models, representing two specimens previously tested experimentally, are then developed to illustrate how interface elements may be used to model mixed mode delamination. The previously discussed panel is revisited, and a global-local modelling approach used to model the skin-stiffener interface. FE models of a stiffened cylindrical shell are also considered, and again the postbuckling characteristics of the shell are compared with experimental results. . The thesis then moves on to optimization of composite structures. This starts off with a literature review of existing optimization methodologies. A Genetic Algorithm (GA) is devised to increase the damage resistance of the I-stiffened panel. The global-local ABAQUS model discussed earlier is used in conjunction with the GA in order to find a revised stacking sequence of both the panel flanges and skin so as to minimize skin-stiffener debonding subject to a variety of design constraints. A second optimization is then presented, this time linked to the FE model of the stiffened cylindrical shell. The objective is to increase the collapse load of the shell, again subject to specific design constraints. The thesis concludes by summarising the importance of the work conducted. FE models were created and validated against experimental work in order to model a variety of composite stiffened structures in their buckling and postbuckling regimes. These models were able to capture the failure characteristics of these structures relating to delamination at the skin-stiffener interface, a phenomenon widely observed experimentally. Various optimizations, able to account for failure mechanisms which may occur prior to overall structural collapse, were then conducted on the analysed structures in order to obtain more damage resistant designs.

Active control of vibration in structures has been investigated by an increasing number of researchers in recent years. There has been a great deal of theoretical work and some experiment examining the use of point forces for vibration control, and more recently, the use of thin piezoelectric crystals laminated to the surfaces of structures. However, control by point forces is impractical, requiring large reaction masses, and the forces generated by laminated piezoelectric crystals are not sufficient to control vibration in large and heavy structures. The control of flexural vibrations in stiffened structures using piezoceramic stack actuators placed between stiffener flanges and the structure is examined theoretically and experimentally in this thesis. Used in this way, piezoceramic actuators are capable of developing much higher forces than laminated piezoelectric crystals, and no reaction mass is required. This thesis aims to show the feasibility of active vibration control using piezoceramic actuators and angle stiffeners in a variety of fundamental structures. The work is divided into three parts. In the first, the simple case of a single actuator used to control vibration in a beam is examined. In the second, vibration in stiffened plates is controlled using multiple actuators, and in the third, the control of vibration in a ring-stiffened cylinder is investigated. In each section, the classical equations of motion are used to develop theoretical models describing the vibration of the structures with and without active vibration control. The effects of the angle stiffener(s) are included in the analysis. The models are used to establish the quantitative effects of variation in frequency, the location of control source(s) and the location of the error sensor(s) on the achievable attenuation and the control forces required for optimal control. Comparison is also made between the results for the cases with multiple control sources driven by the same signal and with multiple independently driven control sources. Both finite and semi-finite structures are examined to enable comparison between the results for travelling waves and standing waves in each of the three structure types. This thesis attempts to provide physical explanations for all the observed variations in achievable attenuation and control force(s) with varied frequency, control source location and error sensor location. The analysis of the simpler cases aids in interpreting the results for the more complicated cases. Experimental results are given to demonstrate the accuracy of the theoretical models in each section. Trials are performed on a stiffened beam with a single control source and a single error sensor, a stiffened plate with three control sources and a line of error sensors and a ring-stiffened cylinder with six control sources and a ring of error sensors. The experimental results are compared with theory for each structure for the two cases with and without active vibration control.
Thesis (Ph.D.)--Mechanical Engineering, 1995.

The structural optimization of a cantilever aircraft wing with curvilinear spars and ribs and stiffeners is described. The design concept of reinforcing the wing structure using curvilinear stiffening members has been explored due to the development of novel manufacturing technologies like electron-beam-free-form-fabrication (EBF3). For the optimization of a complex wing, a common strategy is to divide the optimization procedure into two subsystems: the global wing optimization which optimizes the geometry of spars, ribs and wing skins; and the local panel optimization which optimizes the design variables of local panels bordered by spars and ribs. The stiffeners are placed on the local panels to increase the stiffness and buckling resistance. The panel thickness, size and shape of stiffeners are optimized to minimize the structural weight. The geometry of spars and ribs greatly influences the design of stiffened panels. During the local panel optimization, the stress information is taken from the global model as a displacement boundary condition on the panel edges using the so-called "Global-Local Approach". The aircraft design is characterized by multiple disciplines: structures, aeroelasticity and buckling. Particle swarm optimization is used in the integration of global/local optimization to optimize the SpaRibs. The interaction between the global wing optimization and the local panel optimization is usually computationally expensive. A parallel computing technology has been developed in Python programming to reduce the CPU time. The license cycle-check method and memory self-adjustment method are two approaches that have been applied in the parallel framework in order to optimize the use of the resources by reducing the license and memory limitations and making the code robust. The integrated global-local optimization approach has been applied to subsonic NASA common research model (CRM) wing, which proves the methodology's application scaling with medium fidelity FEM analysis. Both the global wing design variables and local panel design variables are optimized to minimize the wing weight at an acceptable computational cost. The structural weight of the wing has been, therefore, reduced by 40% and the parallel implementation allowed a reduction in the CPU time by 89%. The aforementioned Global-Local Approach is investigated and applied to a composite panel with crack at its center. Because of composite laminates' heterogeneity, an accurate analysis of these requires very high time and storage space. In the presence of structural discontinuities like cracks, delaminations, cutouts etc., the computational complexity increases significantly. A possible alternative to reduce the computational complexity is the global-local analysis which involves an approximate analysis of the whole structure followed by a detailed analysis of a significantly smaller region of interest. We investigate here the performance of the global-local scheme based on the finite element method by comparing it to the traditional finite element method. To do so, we conduct a 2D structural analysis of a composite square plate, with a thin rectangular notch at its center, subjected to a uniform transverse pressure, using the commercial software ABAQUS. We show that the presence of the thin notch affects only the local response of the structure and that the size of the affected area depends on the notch length. We investigate also the effect of the notch shape on the response of the structure. Stiffeners attached to composite panels may significantly increase the overall buckling load of the resultant stiffened structure. Buckling analysis of a composite panel with attached longitudinal stiffeners under compressive loads is performed using Ritz method with trigonometric functions. Results are then compared to those from ABAQUS FEA for different shell elements. The case of composite panel with one, two, and three stiffeners is investigated. The effect of the distance between the stiffeners on the buckling load is also studied. The variation of the buckling load and buckling modes with the stiffeners' height is investigated. It is shown that there is an optimum value of stiffeners' height beyond which the structural response of the stiffened panel is not improved and the buckling load does not increase. Furthermore, there exist different critical values of stiffener's height at which the buckling mode of the structure changes. Next, buckling analysis of a composite panel with two straight stiffeners and a crack at the center is performed. Finally, buckling analysis of a composite panel with curvilinear stiffeners and a crack at the center is also conducted. ABAQUS is used for these two examples and results show that panels with a larger crack have a reduced buckling load. It is shown also that the buckling load decreases slightly when using higher order 2D shell FEM elements. A damage tolerance framework, EBF3PanelOpt, has been developed to design and analyze curvilinearly stiffened panels. The framework is written with the scripting language PYTHON and it interacts with the commercial software MSC. Patran (for geometry and mesh creation), MSC. Nastran (for finite element analysis), and MSC. Marc (for damage tolerance analysis). The crack location is set to the location of the maximum value of the major principal stress while its orientation is set normal to the major principal axis direction. The effective stress intensity factor is calculated using the Virtual Crack Closure Technique and compared to the fracture toughness of the material in order to decide whether the crack will expand or not. The ratio of these two quantities is used as a constraint, along with the buckling factor, Kreisselmeier and Steinhauser criteria, and crippling factor. The EBF3PanelOpt framework is integrated within a two-step Particle Swarm Optimization in order to minimize the weight of the panel while satisfying the aforementioned constraints and using all the shape and thickness parameters as design variables. The result of the PSO is used then as an initial guess for the Gradient Based Optimization using only the thickness parameters as design variables. The GBO is applied using the commercial software VisualDOC.
Ph. D.

Noise and vibration suppression is an important aspect in the design process of structures and machines. Undesirable vibrations can cause fatigue in a structure and are, therefore, a risk to the safety of a structure. One of the most effective and widely used methods of mitigating these unwanted vibrations from a system is passive damping, by using a viscoelastic material. This dissertation will primarily focus on constrained layer passive damping treatments in structures and the investigation of associated complex modes. The key idea behind constrained damping treatment is to increase damping as affected by the presence of a highly damped core layer vibrating mainly in shear. Our main goal was to incorporate viscoelastic material in a thick stiffened panel with plate-strip stiffeners, to enhance the damping characteristics of the structure. First, we investigated complex damped modes in beams in the presence of a viscoelastic layer sandwiched between two elastic layers. The problem was solved using two approaches, (1) Rayleigh beam theory and analyzed using the principle of virtual work, and (2) by using 2D plane stress elasticity based finite-element method. The damping in the viscoelastic material was modeled using the complex modulus approach. We used FEM without any kinematic assumptions for the transverse shear in both the core and elastic layers. Moreover, numerical examples were studied, by including complex modulus in the base and constraining layers. The loss factor was calculated by modal strain energy method, and by solving a complex eigenvalue problem. The efficiency of the modal strain energy method was tested for different loss factors in the core layer. Complex mode shapes of the beam were also examined in the study, and a comparison was made between viscoelastically damped and non-proportionally damped structures. Secondly, we studied the free vibration response of an integrally stiffened and/or stepped plate. The stiffeners used here were plate-strip stiffeners, unlike the rib stiffeners often investigated by researchers. Both plate and stiffeners were analyzed using the first-order shear deformation theory. The deflections and rotations were assumed as a product of Timoshenko beam functions, chosen appropriately according to the given boundary conditions. Unlike Navier and Levy solution techniques, the approach used here can also be applied to fully clamped, free and cantilever supported stiffened plates. The governing differential equations were solved using the Rayleigh-Ritz method. The development of the stiffness and the mass matrices in the Ritz analysis was found to consume a huge amount of CPU time due to the recursive integration of Timoshenko beam functions. An approach is suggested to greatly decrease this amount of CPU time, by replacing the recursive integration in a loop structure in the computer program, with the analytical integration of the integrand in the loop. The numerical results were compared with the exact solutions available in the literature and the commercially available finite-element software ABAQUS. Some parametric studies were carried out to show the influence of certain important parameters on the overall natural frequencies of the stiffened plate. Finally, we investigated the damped response of an adhesively bonded plate employing plate-strip stiffeners, using FSDT for both the plate and stiffeners. The problem was analyzed using the principle of virtual work. At first, we did not consider damping in the adhesive in order to validate our code, by comparing our results with those available in the literature as well as with the results obtained using ABAQUS 3D model. The results were found to be highly satisfactory. We also considered the effect of changing the stiffness of the adhesive layer on the vibration of the bonded system. As a second step, we included damping in the stiffened structure using complex modulus approach, a widely used technique to represent the rheology of the viscoelastic material. We observed an overall increase in the natural frequencies of the system, due to the damping provided by the viscoelastic material. Moreover, it was noticed that when the thickness of the adhesive layer is increased, the natural frequencies and loss factor of the stiffened structure decrease. A viscoelastic material with high loss factor and small thickness will be a perfect design variable to obtain overall high damping in the structure.
Ph. D.

Includes bibliographical references. .
A FEM-based parametric study is undertaken to investigate the buckling behavior of meridionally and circumferentially stiffened steel cylindrical and conical shell frustum subjected to different load cases. This situation arises in different steel shell applications such as storage vessels (liquid, solid and gas) and in certain configurations of industrial process facilities. The stiffeners are flat strips of rectangular section welded on to the outer surface of the shell, either over the whole length of the shell meridian or around the circumference of the shell. It is required to establish how the elastic buckling load and mode shapes vary with respect to certain key parameters of the problem. The parameters of interest in the study include the number of stiffeners around the shell circumference and along the meridian, the stiffener-depth to shell-thickness ratio, and the stiffener depth-to-width ratio. This thesis reports the findings of the parametric study and also presents some results of experimental tests on laboratory small-scale models of stiffened cylindrical and conical frusta.

The European Commission 6th Framework Project COCOMAT (Improved MATerial Exploitation at Safe Design of COmposite Airframe Structures by Accurate Simulation of COllapse) was a four and a half year project (2004 to mid-2008) aimed at exploiting the large reserve of strength in composite structures through more accurate prediction of collapse. In the experimental work packages, significant statistical variation in buckling behaviour and ultimate loading were encountered. The variations observed in the experimental results were not predicted in the finite element analyses that were done in the early stages of the project. The work undertaken in this thesis to support the COCOMAT project was initiated when it was recognised that there was a gap in knowledge about the effect of initial defects and variations in the input variables of both the experimental and simulated panels. The work involved the development of stochastic algorithms to relate variations in boundary conditions, material properties and geometries to the variation in buckling modes and loads up to first failure. It was proposed in this thesis that any future design had to focus on the dominant parameters affecting the statistical scatter in the results to achieve lower sensitivity to variation. A methodology was developed for designing stiffened composite panels with improved robustness. Several panels tested in the COCOMAT project were redesigned using this approach to demonstrate its applicability. The original contributions from this thesis are therefore the development of a stochastic methodology to identify the impact of variation in input parameters on the response of stiffened composite panels and the development of Robust Indices to support the design of new panels. The stochastic analysis included the generation of metamodels that allow quantification of the impact that the inputs have on the response using two first order variables, Influence and Sensitivity. These variables are then used to derive the Robust Indices. A significant outcome of this thesis was the recognition in the final report for COCOMAT that the development of a validated robust index should be a focus of any future design of postbuckling stiffened panels.

This dissertation discusses the thermomechanical analyses performed on threaded fasteners and curvilinearly stiffened composite panels with internal cutouts. The former problem was analyzed using a global/local approach using the commercial finite element software ANSYS while a fully functional code using isogeometric analysis was developed from scratch for the latter. For the threaded fasteners, a global simplified 3D model is built to evaluate the deformation of the structure. A second local model reproducing accurately the threads of the fasteners is used for the accurate assessment of the stresses in the vicinity of the fasteners. The isogeometric analysis code, capable of performing static, buckling and vibration analysis on stiffened composite plates with cutouts using single patch, multiple patches and level set methods is then discussed. A novel way to achieve displacement compatibility between the panel and stiffeners interfaces is introduced. An easy way of modeling plates with complicated cutouts by using edge curves and generating a ruled NURBS surface between them is described. Influence on the critical thermal buckling load and the fundamental mode of vibration due to the presence of circular, elliptical and complicated cutouts is also investigated. Results of parametric studies are presented which show the influence of ply orientation, size and orientation of the cutout, and the position and profile of the curvilinear stiffener. The numerical examples show high reliability and efficiency when compared with other published solutions and those obtained using ABAQUS, a commercial software.
PHD

In this study two dimensional steel frames, reinforced with un-stiffened thin steel panels, are investigated. In the first part of the study, the strip model, a method for analyzing un-stiffened thin steel plate shear walls, was investigated. Sensitivity studies to investigate the influence of the number of strip members to be used to in the strip model and their angle of inclination were conducted. In the second part, responses of various un-stiffened steel plate shear wall systems to lateral loads were investigated. The influences of three major parameters were studied. These are the beam-to-column connection type, the boundary frame stiffness and the plate slenderness ratio (the ratio of the centerline column spacing to the thickness of the plate). In both parts nonlinear pushover analysis were performed with SAP2000 structural analysis program. In this study, the history of development, theory and advantages of un-stiffened thin steel plate shear walls and recommendations for this lateral load resisting system are presented.

This thesis addresses the understanding of the static strength and behaviour of internally ring stiffened T- and DT-joints under axial brace loading. Initial numerical work verifies the appropriateness of the Finite Element (F.E.) modelling technique and the use of the F.E. Method as an analysis tool. This was achieved through a validation study on both unstiffened and ring stiffened T-joints and on unstiffened DT-joints. There follows four substantial parametric studies on ring stiffened T- and DT-joints which investigate the effect of the variation of the stiffener dimensions of plain and T-shaped stiffeners along with the joint geometrical parameters β and γ on the strength and behaviour of the stiffener and the stiffened joint. Also the number and position of the ring stiffeners are investigated. Findings of the study enabled, where appropriate, the proposal of two methods of strength prediction for the ring stiffener. One uses Plastic Theory to postulate a ring model which is based on a five- or six-hinge failure mechanism for the stiffener, resulting in a virtual Work Equation. For this method it is assumed that a portion of the chord interacts with the stiffener in producing the strength enhancement. The stiffener cross-section is then considered as a T- and an I-section for the plain and T-shaped stiffeners respectively. The other is an empirical equation based on the variation of the non-dimensional stiffener strength with the various influencing non-dimensional parameters. It has been shown that the theoretical method can be compromised when the stiffener parameters exceed the validity range of the predictive method whereas the empirical method appears to be more robust to extrapolation of the validity ranges. Both methods provide accurate predictions of stiffener strength when compared to the newly created FE database and existing test and numerical results.

Thesis (Ph. D.)--University of Florida, 1999.
Title from first page of PDF file. Document formatted into pages; contains xv, 209 p.; also contains graphics. Vita. Includes bibliographical references (p. 180-192).

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

In this study a methodology is developed for the fatigue and fracture analysis of helicopter fuselage structures, which are considered as the stiffened panels. The damage tolerance behavior of the stiffened panels multiaxially loaded is investigated by implementing virtual crack closure technique (VCCT). Validation of VCCT is done through comparison between numerical analysis and the studies from literature, which consists of stiffened panels uniaxially loaded and the panel with an inclined crack. A program based on Fortran programming language is developed to automate the crack growth analysis under mixed mode conditions. The program integrates the prediction of the change in crack propagation direction by maximum circumferential stress criterion and the computation of energy release rate by VCCT. It allows reducing the computation time for damage tolerance evaluation for mixed mode cases through finite element analysis and runs the procedure file of MSC.Marc/Mentat for numerical analysis and the program generated by Patran Command Language (PCL) of MSC.Patran for remeshing. The developed code is verified by comparing the crack growth trajectories obtained by numerical analysis with the experimental studies from literature. A submodeling technique is utilized to analyze a particular fuselage portion of helicopter tail boom. Effects of different skin/stringer configurations of the helicopter fuselage structure on stress intensity factor are studied by means of the developed program. Fatigue crack growth analysis is performed by using stress intensity factors obtained from numerical analysis and fatigue propagation models proposed in literature.

In this study, the &ldquo
Free Flexural (or Bending) Vibrations of Stiffened Plates or Panels&rdquo
are investigated in detail. Two different Groups of &ldquo
Stiffened Plates&rdquo
will be considered. In the first group, the &ldquo
Type 4&rdquo
and the &ldquo
Type 6&rdquo
of &ldquo
Group I&rdquo
of the &ldquo
Integrally-Stiffened and/or Stepped-Thickness Plate or Panel Systems&rdquo
are theoretically analyzed and numerically solved by making use of the &ldquo
Mindlin Plate Theory&rdquo
. Here, the natural frequencies and the corresponding mode shapes, up to the sixth mode, are obtained for each &ldquo
Dynamic System&rdquo
. Some important parametric studies are also presented for each case. In the second group, the &ldquo
Class 2&rdquo
and the &ldquo
Class 3&rdquo
of the &ldquo
Bonded and Stiffened Plate or Panel Systems&rdquo
are also analyzed and solved in terms of the natural frequencies with their corresponding mode shapes. In this case, the &ldquo
Plate Assembly&rdquo
is constructed by bonding &ldquo
Stiffening Plate Strips&rdquo
to a &ldquo
Base Plate or Panel&rdquo
by dissimilar relatively thin adhesive layers. This is done with the purpose of reinforcing the &ldquo
Base Plate or Panel&rdquo
by these &ldquo
Stiffening Strips&rdquo
in the appropriate locations, so that the &ldquo
Base Plate or Panel&rdquo
will exhibit satisfactory dynamic response. The forementioned &ldquo
Bonded and Stiffened Systems&rdquo
may also be used to repair a damaged (or rather cracked) &ldquo
Base Plate or Panel&rdquo
. Here in the analysis, the &ldquo
Base Plate or Panel&rdquo
, the &ldquo
Stiffening Plate Strips&rdquo
as well as the in- between &ldquo
adhesive layers&rdquo
are assumed to be linearly elastic continua. They are assumed to be dissimilar &ldquo
Orthotropic Mindlin Plates&rdquo
. Therefore, the effects of shear deformations and rotary moments of inertia are considered in the theoretical formulation. In each case of the &ldquo
Group I&rdquo
and &ldquo
Group II&rdquo
problems, the &ldquo
Governing System of Dynamic Equations&rdquo
for every problem is reduced to the &ldquo
First Order Ordinary Differential Equations&rdquo
. In other words the &ldquo
Free Vibrations Problem&rdquo
, in both cases, is an &ldquo
Initial and Boundary Value Problem&rdquo
is reduced to a &ldquo
Two- Point or Multi-Point Boundary Value Problem&rdquo
by using the present &ldquo
Solution Technique&rdquo
. For this purpose, these &ldquo
Governing Equations&rdquo
are expressed in &ldquo
compact forms&rdquo
or &ldquo
state vector&rdquo
forms. These equations are numerically integrated by the so-called &ldquo
Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials)&rdquo
. In the numerical results, the mode shapes together with their corresponding non-dimensional natural frequencies are presented up to the sixth mode and for various sets of &ldquo
Boundary Conditions&rdquo
for each structural &ldquo
System&rdquo
. The effects of several important parameters on the natural frequencies of the aforementioned &ldquo
Systems&rdquo
are also investigated and are graphically presented for each &ldquo
Stiffened and Stiffened and Bonded Plate or Panel System&rdquo
. Additionally, in the case of the &ldquo
Bonded and Stiffened System&rdquo
, the significant effects of the &ldquo
adhesive material properties&rdquo
(i.e. the &ldquo
Hard&rdquo
adhesive and the &ldquo
Soft&rdquo
adhesive cases) on the dynamic response of the &ldquo
plate assembly&rdquo
are also presented.

Este trabalho verifica, por meio de análises numérico-paramétricas de lajes nervuradas, o quanto a desconsideração (ou a consideração de maneira simplificada) da excentricidade existente entre os eixos das nervuras e o plano médio da capa influencia nos resultados de deslocamentos e esforços atuantes nas peças que compõem estes sistemas. Foram apresentados os conceitos teóricos relativos à cada modelo de cálculo permitido pelas normas técnicas, e foram realizadas análises considerando variações nos seguintes parâmetros: relação entre a altura da capa e a altura total da laje nervurada; relação entre a distância entre os eixos das nervuras e a distância entre os pontos de apoio, e espaçamento entre os eixos das nervuras. Os diferentes modelos mecânicos foram analisados utilizando o método dos elementos finitos, por meio do programa computacional ANSYS 5.5, considerando-se um comportamento elástico-linear para o material concreto armado. Foram relacionados aspectos importantes a serem observados na escolha do modelo adequado, de acordo com os parâmetros analisados, para serem aplicados nos escritórios de cálculo. Verificou-se a necessidade da consideração da excentricidade, seja por modelo realista, ou por modelos simplificados, para a obtenção de resultados numéricos mais próximos do comportamento da estrutura real.
This work verifies, through parametric-numerical analysis of slabs stiffened with ribs, how much the disregard (or regard in a simplified way) of the existent eccentricity between the axis of the ribs and the medium plan of the plate influences on the results of displacements and acting efforts over the parts wich make the system. The theorical concepts related to each model of calculation allowed through technical codes have been presented, and, analysis have been made considering variations in the following parameters: relation between plate height and total height of the waffle slab; relation of distance between the axis of the ribs and the distance between the supporting points, and the gap between the axis of the ribs. Different mechanical models have been analysed using the finite element analysis, through the computer program ANSYS 5.5, considering an elastic-linear behaviour for the reinforced concrete material. Important aspects have been disclosed and should be carefully looked into for an adequate model choice, according to the analysed parameters to be applied in the design\'s offices. The need for eccentricity consideration has been verified, be it by using a realistic model or by simplified models, for close numerical results gathering of the real structural behaviour.

Statistical Energy Analysis (SEA) is one of the methods in literature to estimate high frequency vibrations. The inputs required for the SEA power balance equations are damping and coupling loss factors, input powers to the subsystems. In this study, the coupling loss factors are derived for two and three plates joined with a stiffener system. Simple formulas given in the literature for coupling loss factors of basic junctions are not used and the factors are calculated from the expressions derived in this study. The stiffener is modelled as line mass, Euler beam, and open section channel having double and triple coupling. Plate is modelled as Kirchoff plate. In the classical SEA approach the joint beam is modelled as another subsystem. In this study, the beam is not a separate subsystem but is used as the characteristics of the joint and to calculate the coupling loss factor between coupled plates. Sensitivity of coupling loss factors to system parameters is studied for different beam approaches. The derived coupling loss factors and input powers are used to calculate the subsystem energies by SEA. The last plate is joined to the first one to simulate the fuselage structure. A plate representing floor structure and acoustic volume are also added. The different modelling types are assessed by applying pressure wave excitation. It is shown that deriving the parameters as given in this study increases the efficiency of the SEA method.

Pendant sa mission opérationnelle, un moyen de transport est soumis à des excitations acoustiques, aérodynamiques et structurales à large bande. Les moyens de transport, tels que les avions, les lanceurs spatiaux, les bateaux, les voitures, les trains, etc., sont conçus pour accomplir un objectif principal, généralement de transférer une charge utile (passagers, marchandises, satellites, par exemple) d’un point à un autre, en maintenant toujours un niveau élevé de confort, de sécurité et de capacité de survie de la charge utile. Les réglementations nationales et internationales en matière de pollution sonore sont de plus en plus strictes ; les scientifiques et les acteurs industriels sont confrontés à ces défis de développement de nouveaux matériaux et de nouveaux choix de conception.Les matériaux composites, les géométries complexes et les nouvelles conceptions sont étudiés, ce qui rend l’étude et la prédiction de la réponse vibro-acoustique de ces structures un défi énorme. La complexité rend la dérivation des modèles analytiques plus difficile à obtenir ; l’utilisation d’outils numériques est d’une importance cruciale. L’une des méthodes les plus utilisées est la modélisation par éléments finis (FE), mais l’énorme quantité de degrés de liberté associée à un coût de calcul élevé limite son utilisation dans la gamme de basses fréquences. Au cours des dernières décennies, différentes méthodes sont dérivées pour obtenir les caractéristiques de dispersion des structures ; l’une des plus courantes est la méthode des éléments finis ondulatoire (WFEM), qui est basée sur la propagation des ondes. Cette méthode a été appliquée sur diverses structures simples et complexes, dérivant une formulation soit 1D que 2D, également étendu à des structures courbes.Récemment, une approche énergétique a été dérivée à partir de la méthode de Prony : la méthode de corrélation d’onde inhomogène (IWC). Cette approche trouve son applicabilité dans la gamme de fréquence moyenne et haute, où le chevauchement modal est assez élevé. La méthode IWC est basée sur la projection du champ d’onde sur une onde itinérante inhomogène. Le nombre d’onde dominant, à chaque fréquence, est obtenu par maximisation de la fonction de corrélation entre le champ d’onde projet\'e et l’onde inhomogène.Dans ce contexte, une version étendue de la méthode IWC est dérivée, permettant de décrire les courbes de dispersion des structures complexes : plaques étroites périodiques, plaques composites, panneaux raidis, panneaux composites courbes et panneaux raidis courbes. La méthode a l’avantage d’être applicable dans un environnement opérationnel, en utilisant des emplacements d’acquisition clairsemés. Une analyse complète des caractéristiques de dispersion est effectuée, même en présence d’éléments périodiques et de dispositifs de contrôle des vibrations, décrivant les écarts de bande directement corrélés dans certaines régions de fréquence et l’atténuation du niveau de vibration. Une estimation numérique et expérimentale du facteur de perte d’amortissement structurel est calculée. Une description de la dynamique locale en présence de résonateurs à petite échelle, de l’effet de la périodicité et de l’identification du comportement multimodale sont également capturés.Tous les résultats des simulations numériques sont validés expérimentalement sur des meta-structures complexes à grande échelle, comme un panneau sandwich imprimé en 3D, un panneau courbé sandwich en composite et un panneau d'avion en aluminium. L’effet des résonateurs à petite échelle imprimés en 3D à orientation industrielle sur la réponse vibro-acoustique des structures considérées est réalisé en tenant compte soit de l'excitation champ acoustique diffus et de l'excitations mécaniques
During its operational mission, a transportation mean is subject to broadband acoustic, aerodynamic and structure-borne excitations. The transportation means, such as aircrafts, space launchers, ships, cars, trains, etc., are designed to accomplish a primary goal, usually to transfer a payload (passengers, goods, satellites, for example) from a point to another, always keeping a high level of comfort, safety and survivability of the payload. National and international regulations about noise pollution are more and more stringent; scientists and industrial players are facing with these challenges developing new materials and new design choices. Composite materials, complex geometries and new design concepts are investigated, making the analysis and the prediction of the vibroacoustic response of these structures a huge challenge. The complexity makes the derivation of analytical models harder to obtain; the use of numerical tools is of crucial importance. One of the most employed method is the Finite Element (FE) modeling, but the huge amount of degrees of freedom together with a high computational cost limits its use in the low frequency range. In the last decades, different methods are derived to obtain the dispersion characteristics of the structures; one of the most common is the Wave Finite Element Method (WFEM), that is based on the wave propagation. This method has been applied on various simple and complex structures, deriving both 1D and 2D formulations, extended also to curved structures. Recently, an energetic approach has been derived starting from the Prony’s method, the Inhomogeneous Wave Correlation (IWC) method. This approach has its applicability in the mid-high frequency range, where the modal overlap is quite high. The IWC method is based on the projection of the wavefield on an inhomogeneous traveling wave. The dominant wavenumber, at each frequency, is obtained by maximization of the correlation function between the projected wavefield and the inhomogeneous wave. In this context, an extended version of the IWC method is derived, allowing to describe the dispersion curves of complex structures: periodic narrow plates, composite plates, ribbed panels, composite curved shells and curved stiffened structures. The method has the advantage to be applied in an operational environment, making use of sparse acquisition locations. A complete dispersion characteristics analysis is conducted, even in presence of periodic elements and vibration-control devices, describing the directly correlated band-gaps in certain frequency regions and general vibration level attenuation. A numerical and experimental estimation of the structural damping loss factor is computed. A description of the local dynamics in presence of small-scale resonators, of the periodicity effect and the identification of the multi-modal behavior are also captured. All the results of the numerical simulations are experimentally validated on complex large-scale meta-structures, such as a 3D-printed sandwich panel, a curved composite laminated sandwich panel and a aluminum aircraft sidewall panel. The effect of industrially-oriented 3D-printed small-scale resonators on the vibro-acoustic response of the considered structures is conducted, taking in account both diffuse acoustic field and mechanical excitations
Tijdens zijn operationele opdracht, is een vervoersgemiddelde onderworpen aan breedband akoestische, aërodynamische en structuur - gedragen excitaties. De transportmiddelen, zoals vliegtuigen, ruimtelanceerders, schepen, auto’s, treinen, enz., zijn ontworpen om een primair doel te verwezenlijken, gewoonlijk om een lading (passagiers, goederen, satellieten, bijvoorbeeld) van een punt naar een andere over te brengen, altijd houdend een hoog niveau van comfort, veiligheid en overleefbaarheid van de lading. De nationale en internationale regelgeving inzake geluidshinder is steeds strenger; wetenschappers en industriële spelers worden geconfronteerd met deze uitdagingen bij de ontwikkeling van nieuwe materialen en nieuwe ontwerpkeuzes. Samengestelde materialen, complexe geometrieën en nieuwe ontwerpconcepten worden onderzocht, waardoor de studie en de voorspelling van de vibroakoestische respons van deze structuren een enorme uitdaging. De complexiteit maakt de afleiding van analytische modellen moeilijker te verkrijgen; het gebruik van numerieke tools is van cruciaal belang. Een van de meest gebruikte methoden is de FE-modellering (Finite Element), maar de enorme hoeveelheid vrijheidsgraden in combinatie met hoge computerkosten beperkt het gebruik ervan in het lage frequentiebereik. In de afgelopen decennia zijn verschillende methoden afgeleid om de verspreidingskenmerken van de structuren te verkrijgen; een van de meest voorkomende methoden is de Wave Finite element Method (WFEM), die gebaseerd is op de golfvoortplanting. Deze methode is toegepast op verschillende eenvoudige en complexe structuren, die een 1D- en 2D-formulering afleiden, ook uitgebreid tot gebogen structuren. Onlangs is een energieke benadering afgeleid van de methode van Prony, de Inhomogeneous Wave Correlation (IWC) methode. Deze benadering heeft haar toepasbaarheid in het middenhoge frequentiebereik, waar de modale overlapping vrij hoog is. De IWC-methode is gebaseerd op de projectie van het golfveld op een inhomogene golf. De dominante golvenumber wordt bij elke frequentie verkregen door maximalisatie van de correlatiefunctie tussen het geprojecteerde golfveld en de inhomogene golf. In dit verband wordt een uitgebreide versie van de IWC-methode afgeleid, waarmee de verspreidingscurves van complexe structuren kunnen worden beschreven: Periodieke smalle platen, samengestelde platen, geribde panelen, samengestelde gebogen schalen en gebogen geribbelde panelen. De methode heeft het voordeel om te worden toegepast in een operationele omgeving, waarbij gebruik wordt gemaakt van sparse acquisitielocaties. Er wordt een volledige analyse van de verspreidingskenmerken uitgevoerd, zelfs in aanwezigheid van periodieke elementen en apparatuur voor trillingscontrole, die de direct met elkaar verband houdende bandhiaten in bepaalde frequentiegebieden en de verzwakking van het trillingsniveau beschrijven. Er wordt een numerieke en expexiii rimentele schatting van de verliesfactor van de structurele demping berekend. Een beschrijving van de lokale dynamiek in aanwezigheid van kleinschalige resonatoren, van het periodiciteitseffect en de identificatie van het multimodale gedrag worden ook vastgelegd. Alle resultaten van de numerieke simulaties worden experimenteel gevalideerd op complexe grootschalige meta-structuren, zoals een 3D-gedrukt sandwichpaneel, een gebogen samengesteld gelamineerd sandwichpaneel en een aluminium zijpaneel aan de zijkant van het vliegtuig. Het effect van industrieel georiënteerde 3D-gedrukte kleinschalige resonatoren op de trillings-akoestische respons van de overwogen structuren wordt uitgevoerd, waarbij rekening wordt gehouden met zowel diffuus akoestisch veld als mechanische excitaties

A high-order hybrid discontinuous Galerkin finite element method (DG-FEM) is developed for multi-layered curved panels having large deformation and finite strain. The kinematics of the multi-layered shells is presented at first. The Jacobian matrix and its determinant are also calculated. The weak form of the DG-FEM is next presented. In this case, the discontinuous basis functions can be employed for the displacement basis functions. The implementation details of the nonlinear FEM are next presented. Then, the Consistent Orthogonal Basis Function Space is developed. Given the boundary conditions and structure configurations, there will be a unique basis function space, such that the mass matrix is an accurate diagonal matrix. Moreover, the Consistent Orthogonal Basis Functions are very similar to mode shape functions. Based on the DG-FEM, three dedicated finite elements are developed for the multi-layered pipes, curved stiffeners and multi-layered stiffened hydrofoils. The kinematics of these three structures are presented. The smooth configuration is also obtained, which is very important for the buckling analysis with large deformation and finite strain. Finally, five problems are solved, including sandwich plates, 2-D multi-layered pipes, 3-D multi-layered pipes, stiffened plates and stiffened multi-layered hydrofoils. Material and geometric nonlinearities are both considered. The results are verified by other papers' results or ANSYS.
Master of Science

Unitized aircraft structures have the potential to be more efficient than current aircraft structures. The Electron Beam Freeform Fabrication (EBF3) process can be used to manufacture unitized aircraft structures. The structural efficiency of blade stiffened panels made with EBF3 was compared to panels made by integrally machining from thick plate. The panels were tested under two load cases in a combined compression-shear load test fixture. One load case tested the panels' responses to a higher compressive load than the shear load. The second load case tested the panels' responses to an equal compressive and shear load. Finite element analysis was performed to compare with the experimental results. The EBF3 panels failed at a 18.5% lower buckling load than the machined panels when loaded mostly in compression but at an almost two times higher buckling load than the machined panels when the shear matched the compressive load. The finite element analysis was in good agreement with the experimental results prior to buckling. The results demonstrate that the EBF3 process has the capabilities of manufacturing stiffened panels that behave similarly to machined panels prior to buckling. Once the EBF3 panels buckled, the buckled shape of the EBF3 panels was different from the machined panels, generally buckling in the opposite direction of what was observed with the machined panels. This was also expected based on the finite element analysis. The different post-buckling response between the two manufacturing techniques was attributed to the residual stress and associated distortion induced during the EBF3 manufacturing process.
Master of Science

The Element Free Galerkin (EFG) method, which is based on the Moving Least Squares (MLS) approximation, is developed here for vibration, buckling and static analysis of homogenous and FGM plate with curvilinear stiffeners. Numerical results for different stiffeners configurations and boundary conditions are presented. All results are verified using the commercial finite element software ANSYS® and other available results in literature. In addition, the vibration analysis of plates with curvilinear stiffeners is carried out using Ritz method. A 24 by 28 in. curvilinear stiffened panel was machined from 2219-T851 aluminum for experimental validation of the Ritz and meshfree methods of vibration mode shape predictions. Results were obtained for this panel mounted vertically to a steel clamping bracket using acoustic excitation and a laser vibrometer. Experimental results appear to correlate well with the meshfree and Ritz method results. In reality, many engineering structures are subjected to random pressure loads in nature and cannot be assumed to be deterministic. Typical engineering structures include buildings and towers, offshore structures, vehicles and ships, are subjected to random pressure. The vibrations induced from gust loads, engine noise, and other auxiliary electrical system can also produce noise inside aircraft. Consequently, all flight vehicles operate in random vibration environment. These random loads can be modeled by using their statistical properties. The dynamical responses of the structures which are subjected to random excitations are very complicated. To investigate their dynamic responses under random loads, the meshfree method is developed for random vibration analysis of curvilinearly-stiffened plates . Since extensive efforts have been devoted to study the buckling and vibration analysis of stiffened panel to maximize their natural frequencies and critical buckling loads, these structures are subjected to in-plane loading while the vibration analysis is considered. In these cases the natural frequencies calculated by neglecting the in-plane compression are usually over predicted. In order to have more accurate results it might be necessary to take into account the effects of in-plane load since it can change the natural frequency of plate considerably. To provide a better view of the free vibration behavior of the plate with curvilinear stiffeners subjected to axial/biaxial or shear stresses several numerical examples are studied. The FEM analysis of curvilinearly stiffened plate is quite computationally expensive, and the meshfree method seems to be a proper substitution to reduce the CPU time. However it will still require many simulations. Because of the number of simulations may be required in the solution of an engineering optimization problem, many researchers have tried to find approaches and techniques in optimization which can reduce the number of function evaluations. In these problems, surrogate models for analysis and optimization can be very efficient. The basic idea in surrogate model is to reduce computational cost and giving a better understanding of the influence of the design variables on the different objectives and constrains. To use the advantage of both meshfree method and surrogate model in reducing CPU time, the meshfree method is used to generate the sample points and combination of Kriging (a surrogate model) and Genetic Algorithms is used for design of curvilinearly stiffened plate. The meshfree and kriging results and CPU time were compared with those obtained using EBF3PanelOpt.
Ph. D.

Les lisses des avions de nouvelle génération seront collées (collage ou co-cuisson) à la peau de fuselage. L'objectif de ce travail est d'étudier les liaisons entre les raidisseurs et la peau afin d'assurer le transfert des efforts durablement en particulier dans les phases de post-flambement des structures. Dans un premier temps, une campagne d'essais est menée sur des assemblages " peau/semelles de raidisseurs ". L'influence de la température, du vieillissement ainsi que le comportement en fatigue sont étudiés. Des modèles numériques industrialisables sont mis en place et montrent qu'ils permettent de corréler de façon satisfaisante les résultats d'essais à la fois en statique et en fatigue. Dans un deuxième temps, des essais de flexion trois et quatre points portant sur des assemblages " peau/raidisseurs complets " permettent de dégager les spécificités relatives aux raidisseurs en forme d'oméga ainsi que l'influence des coins de résine liés au mode de fabrication. Des essais spécifiques de flexion sept points montrent les effets de la flexion bi-axiale rencontrée dans les phases de post-flambement des structures. Des études numériques complètent l'analyse et valident les critères de décollement au niveau structural. Une approche " global/local " permettant de diminuer de façon considérable les temps de calcul est ensuite proposée et validée. Pour finir, deux études portant sur des essais de post-flambement sur des panneaux raidis en compression et cisaillement sont effectuées. L'analyse de ces essais permet de valider l'ensemble des méthodes développées au cours de l'étude et de tirer les principales conclusions
For composite fuselage applications, stringers will be bonded to the skin. The aim of this work is to study skin to stringers attachments in order to ensure load transfers mainly during post-buckling phases and taking into account environmental effects and fatigue. Firstly, a test campaign was launched on "skin/stringer flanges". Influences of temperature, ageing and fatigue behaviour have been studied. Numerical models adapted to industrial requirements have been set up and allow a good correlation between tests and calculations in fatigue and static. Secondly, three and four points bending tests on "skin/full stringers" assemblies were performed and demonstrated the particularities of omega stringers and the influence of resin fillets linked to the manufacturing process. Furthermore, specific seven points bending tests show effects of biaxial bending observed during post-buckling phases. For all the tests performed, numerical studies allow the validation of the debonding criterion previously developed and a global/local approach is proposed at structural level. Finally, two stiffened panels were tested in compression and shear. The post-buckling behaviour is studied and allows the validation of the methods developed during the study and provides the main conclusions

Concevoir des structures au regard de leur comportement mécanique est une tâche importante en ingénierie. Cependant, cette phase de conception peut s'avérer longue et fastidieuse lorsque les relations de cause à effet ne sont pas correctement identifiées. Plus spécifiquement, il est généralement difficile d’obtenir la meilleure forme d’une structure (la forme optimale), car cela fait appel à de nombreuses compétences. En effet, des outils avancés pour la modélisation géométrique sont nécessaires pour représenter fidèlement la structure et pour explorer une large variété de formes. A cela s’ajoute le besoin d’une méthode de calcul de structures compétente et rapide afin de réduire la durée du processus d’optimisation. Un lien étroit entre le modèle géométrique et celui d’analyse est souhaité car tous deux sont amenés à communiquer successivement. Ainsi, l’Analyse IsoGéométrique apparaît comme un outil adéquat pour les problèmes d’optimisation paramétrique de formes. En effet, cette méthode s’appuie sur un modèle unique pour décrire fidèlement la géométrie et pour effectuer l’analyse. Entièrement basée sur le concept de l’AIG, nous construisons une stratégie de conception optimale de la forme pour les structures raidies, omniprésentes en aéronautique. Nous présentons une formulation massif coque permettant d’imposer des variations continues d’épaisseur à une structure mince. Nous formulons des sensibilités analytiques pour les éléments isogéométriques standards et coques. Aussi, nous présentons une approche immergée pour appliquer des changements de forme aux structures raidies. Du point de vue de l’analyse, nous construisons un algorithme dédié aux cas de discrétisations non-conformes en s'appuyant sur les méthodes de couplage Mortar et de décomposition de domaine. In fine, tous ces développements sont fusionnés et permettent de traiter divers exemples avec des niveaux de complexité croissants
Designing structural parts against the material limits, the impact of loads, and many other constraints, is of standard interest in engineering. However, improving the design of a structure can be long and drawn out, especially when a clear understanding of cause-effect relationships is missing. Finding the best possible design, namely the optimal design, is a complex task because it requires several competences. Usually, efficient geometric modeling is needed to accurately represent the structure. Conjointly, the geometric model should provide high flexibility during the design exploration. In addition, structural analysis must be fast enough to shorten the overall process. Besides, for the sake of compactness, a close connection between the geometric model and the structural analysis seems essential. Finally, all modeling choices are deeply related, and thus, they should be thought and built accordingly to the others. Therefore, IsoGeometric Analysis appears as a powerful tool for structural optimization since it uses a unique model with both high quality geometric and analysis properties. Here, we present a compact framework built on the core idea of IGA. We strive to construct unified models with new opportunities for structural design with a direct application to stiffened Aerostructures. More specifically, we present a solid-shell approach to impose continuous thickness variations. We formulate analytical sensitivities for standard and shell formulations. Then, we introduce an embedded technique that enables to impose complex shape updates. From the analysis point of view, we design a specific solver based on Domain Decomposition methods and Mortar approach for the coupling of non-conforming discretizations. Different examples with increasing level of complexity show the performances of the adopted methodologies

Stiffeners attached to composite panels and shells may significantly increase the overall buckling load of the resultant stiffened structure. Initially, an extensive literature review was conducted over the past ten years of published work wherein research was conducted on grid stiffened composite structures and stiffened panels, due to their applications in weight sensitive structures. Failure modes identified in the literature had been addressed and divided into a few categories including: buckling of the skin between stiffeners, stiffener crippling and overall buckling. Different methods have been used to predict those failures. These different methods can be divided into two main categories, the smeared stiffener method and the discrete stiffener method. Both of these methods were used and compared in this thesis. First, a buckling analysis was conducted for the case of a grid stiffened composite pressure vessel. Second, a buckling analysis was conducted under the compressive load on the composite stiffened panels for the case of one, two and three longitudinal stiffeners and then, using different parameters, stiffened panels under combined compressive and shear load for the case of one longitudinal centric stiffener and one longitudinal eccentric stiffener, two stiffeners and three stiffeners.
Master of Science

Vibration and stability studies have been undertaken on glass fibre reinforced polymer composite unstiffened and stiffened plates to optimise their dynamic properties. Boundary conditions, stiffeners and orthotropy of the material add to the complexity of a mathematical solution and to overcome this problem experimental and analytical studies were undertaken. The former method was carried out by impact hammer and an FFT digital signal analyser and the latter method was undertaken using finite element computer software. The current research concentrated upon the procedures and possible techniques available to optimise the dynamic properties of the plate without introducing weight penalty with the object of achieving an efficient structural performance coupled with an economic design. It has been shown that most of the increase in frequency and critical buckling load was directly related to the increase in stiffness of the stiffener and its position on the plate structure. The mode shapes have provided information regarding the most advantageous position for the setting of the stiffeners; they must be positioned away from nodal lines. The effect of the stiffener was significant for the fully clamped and clamped/free plates where only bending modes of vibration are present. However, for the completely free plates, where both bending and torsional modes of vibration could occur, the effect that the stiffeners have on the torsional modes was minimal. To locate precisely the position of the stiffener may be difficult when the plates are subjected to in-plane compressive loads, because higher order mode shapes may interchange. The mass-saving advantage which has been obtained in this research has shown that the stiffened plates with top-hat stiffeners were seen to have higher natural frequencies, within a specific vibration mode, compared to stiffened plates with rectangular stiffeners (blade).

In this research, we apply modern high performance computing techniques to solve an engineering problem, structural analysis of grid stiffened panels. An existing engineering code, SPANDO, is studied and modified to execute more efficiently on high performance workstations and parallel computers. Two new SPANDO packages, a modified sequential SPANDO and parallel SPANDO, are developed. In developing the new sequential SPANDO, we use two existing high performance numerical packages: LAPACK and ARPACK to solve our linear algebra problems. Also, a new block-oriented algorithm for computing the matrix-vector multiplication w=A^{-1}Bx is developed. The experimental results show that the new sequential SPANDO can save over 70% of memory size, and is at least 10 times faster than the original SPANDO. In parallel SPANDO, ScaLAPACK and BLACS are used. There are many factors that may affect the performance of parallel SPANDO. The parallel performance and the affects of these factors are discussed in this thesis.
Master of Science

A utilização de aços de alta resistência em terças formadas a frio faz com que as espessuras sejam cada vez mais reduzidas e, como consequência, os fenômenos de instabilidade mais pronunciados. Para melhorar a eficiência estrutural, enrijecedores longitudinais podem ser inseridos na alma, aumentando a resistência em relação ao modo de instabilidade local. Ainda que a utilização de seções com alma enrijecida seja uma prática comum, os procedimentos adequados para seu dimensionamento são pouco abordados na literatura. O objetivo deste trabalho foi estudar o comportamento estrutural de terças formadas a frio de seção transversal ZAE, com enrijecedores de borda a 90º e dois enrijecedores longitudinais na alma. Para tanto, foram realizadas análises teórica e experimental de um conjunto formado por terças com alma enrijecida ZAE e suas equivalentes de alma plana, as seções Z com enrijecedores de borda a 90°. Apesar de ter sido dada ênfase às solicitações por força cortante e por combinação de momento fletor e força cortante, foram realizados ensaios complementares para avaliar a predominância de momento fletor. As alterações nos esforços críticos elásticos devido à presença dos enrijecedores foram analisadas teoricamente, e os dados experimentais e numéricos foram utilizados para prever a interação. Os resultados teóricos indicaram que os enrijecedores longitudinais têm pequena influência nos modos de instabilidade distorcional e global, porém grande influência no modo local, promovendo um aumento significativo das tensões críticas em relação às seções correspondentes de alma plana. Já os resultados experimentais mostraram que a capacidade resistente das seções Z foi superior a das seções ZAE, devido principalmente à mobilização do campo de tração e à maior restrição rotacional da mesa conferida pela ligação. Os protótipos sem restrição à distorção apresentaram falha prematura, ocasionada pela rotação da mesa na região dos apoios. Considerando os protótipos com restrição à distorção, os resultados atenderam às curvas de interação circular e trilinear. Concluiu-se que o projeto de terças com alma enrijecida pode ser realizado utilizando a expressão de interação trilinear e o momento fletor resistente do modo distorcional.
The use of high strength steel in cold-formed purlins leads to a reduction in thickness and, as a consequence, the instability becomes more significant. In order to improve the structural efficiency of the sections, longitudinal stiffeners can be inserted into the web, increasing the strength in relation to local buckling. Although the use of sections with stiffened web is a common practice, the appropriate procedures for design are rarely discussed in scientific literature. The purpose of this work was to study the structural behavior of cold-formed steel purlins ZAE-sections, with 90º lips and two longitudinal stiffeners in the web. Therefore, theoretical and experimental analyses were performed, involving a set of purlins with stiffened web ZAE-sections and their equivalent plain web, the Z-sections with 90º lips. Although emphasis was given in shear and combined bending and shear, additional experimental tests were performed to evaluate the predominance of bending. Changes in critical elastic buckling stresses due to longitudinal stiffeners were evaluated and experimental and numerical data were used to predict the interation. Theoretical results indicated that longitudinal stiffeners of the ZAE-sections have little influence on distortional and global buckling. However, it has a great influence on local buckling, promoting a significant increase of the critical stresses in relation to the Z-sections. Experimental results showed that the ultimate strength of the Z-sections was higher than ZAE-sections, mainly due to the development of tension field action and the rotational restraint of the web conferred by the connection. The prototypes without distortion restraint presented premature failure, caused by rotation of the web in the region of the supports. Considering the distortion-constrained prototypes, the results satisfied the \"circular\" and \"trilinear\" interaction curves. It was concluded that design of purlins with stiffened web can be performed using the \"trilinear\" interaction expression and the distortional buckling moment capacity.

Thesis (M.S. in Mechanical Engineering)--Naval Postgraduate School, June 1992.
Thesis Advisor: Salinas, David. Description based on title screen as viewed on April 16, 2009. Includes bibliographical references (p. 124). Also available in print.

Spacecraft designs are a result of system properties and design variables that ensure the spacecraft will operate to mission objectives. The focus of this effort is a set of global system variables for frequency, length, total mass and the ratio between the payload mass and the support structure mass. These properties will be explored to observe the behavior of the system and develop relationships that govern the trade-offs between the variables and assist mission planners in future spacecraft design. These variables will be observed in one-dimensional structures where the dominating dimension is many times larger than the other two dimensions and the system is comprised of a support and a payload member. To observe the interaction between the payload and the support, the system was varied for different system variables and observed through ABAQUS finite element software. Attempts were made to predict the system frequency through mathematical approaches. The finite element work was able to generate several approximate relationships between the system variables and the fundamental natural frequency of the system. From these relationships an approximate equation was developed for the frequency for a fixed mass ratio and load ratio as a function of the length, bending stiffness, and total mass of the system. Additional work into the changes to the system as the number of connect points is increased shows the system converging towards a frequency solution which results in a minimized dependence on the connection points. These results were then compared to those of several derived analytical models to determine if a closed-form solution could be used to predict system behavior over the same range of structural characteristics. This closed form solution proved to correlate well to analytical predictions only for the case where the support structure dominates the total system mass, and thus the structural system performs like a beam under compression. Further work is necessary to accurately predict the system frequency through an analytical approach. These insights promise to aid mission designers in objectively evaluating new structural architectures based on structural performance rather than on an unbalanced adherence to heritage or in some cases personal preference.