Tesi sul tema "Structural analysis (engineering)"

Uncertainty involved in the safe and comfort design of the structures is a major concern of civil engineers. Traditionally, the uncertainty has been overcome by utilizing various and relatively large safety factors for loads and structural properties. As a result in conventional design of for example tall buildings, the designed structural elements have unnecessary dimensions that sometimes are more than double of the ones needed to resist normal loads. On the other hand the requirements for strength and safety and comfort can be conflicting. Consequently, an alternative approach for design of the structures may be of great interest in design of safe and comfort structures that also offers economical advantages. Recently, there has been growing interest among the researchers in the concept of structural control as an alternative or complementary approach to the existing approaches of structural design. A few buildings have been designed and built based on this concept. The concept is to utilize a device for applying a force (known as control force) to encounter the effects of disturbing forces like earthquake force. However, the concept still has not found its rightful place among the practical engineers and more research is needed on the subject. One of the main problems in structural control is to find a proper algorithm for determining the optimum control force that should be applied to the structure. The investigation reported in this thesis is concerned with the application of active control to civil engineering structures. From the literature on control theory. (Particularly literature on the control of civil engineering structures) problems faced in application of control theory were identified and classified into two categories: 1) problems common to control of all dynamical systems, and 2) problems which are specially important in control of civil engineering structures. It was concluded that while many control algorithms are suitable for control of dynamical systems, considering the special problems in controlling civil structures and considering the unique future of structural control, many otherwise useful control algorithms face practical problems in application to civil structures. Consequently a set of criteria were set for judging the suitability of the control algorithms for use in control of civil engineering structures. Various types of existing control algorithms were investigated and finally it was concluded that predictive optimal control algorithms possess good characteristics for purpose of control of civil engineering structures. Among predictive control algorithms, those that use ARMA stochastic models for predicting the ground acceleration are better fitted to the structural control environment because all the past measured excitation is used to estimate the trends of the excitation for making qualified guesses about its coming values. However, existing ARMA based predictive algorithms are devised specially for earthquake and require on-line measurement of the external disturbing load which is not possible for dynamic loads like wind or blast. So, the algorithms are not suitable for tall buildings that experience both earthquake and wind loads during their life. Consequently, it was decided to establish a new closed loop predictive optimal control based on ARMA models as the first phase of the study. In this phase it was initially established that ARMA models are capable of predicting response of a linear SDOF system to the earthquake excitation a few steps ahead. The results of the predictions encouraged a search for finding a new closed loop optimal predictive control algorithm for linear SDOF structures based on prediction of the response by ARMA models. The second part of phase I, was devoted to developing and testing the proposed algorithm The new developed algorithm is different from other ARMA based optimal controls since it uses ARMA models for prediction of the structure response while existing algorithms predict the input excitation. Modeling the structure response as an AR or ARMA stochastic process is an effective mean for prediction of the structure response while avoiding measurement of the input excitation. ARMA models used in the algorithm enables it to avoid or reduce the time delay effect by predicting the structure response a few steps ahead. Being a closed loop control, the algorithm is suitable for all structural control conditions and can be used in a single control mechanism for vibration control of tall buildings against wind, earthquake or other random dynamic loads. Consequently the standby time is less than that for existing ARMA based algorithms devised only for earthquakes. This makes the control mechanism more reliable. The proposed algorithm utilizes and combines two different mathematical models. First model is an ARMA model representing the environment and the structure as a single system subjected to the unknown random excitation and the second model is a linear SDOF system which represents the structure subjected to a known past history of the applied control force only. The principle of superposition is then used to combine the results of these two models to predict the total response of the structure as a function of the control force. By using the predicted responses, the minimization of the performance index with respect to the control force is carried out for finding the optimal control force. As phase II, the proposed predictive control algorithm was extended to structures that are more complicated than linear SDOF structures. Initially, the algorithm was extended to linear MDOF structures. Although, the development of the algorithm for MDOF structures was relatively straightforward, during testing of the algorithm, it was found that prediction of the response by ARMA models can not be done as was done for SDOF case. In the SDOF case each of the two components of the state vector (i.e. displacement and velocity) was treated separately as an ARMA stochastic process. However, applying the same approach to each component of the state vector of a MDOF structure did not yield satisfactory results in prediction of the response. Considering the whole state vector as a multi-variable ARMA stochastic vector process yielded the desired results in predicting the response a few steps ahead. In the second part of this phase, the algorithm was extended to non-linear MDOF structures. Since the algorithm had been developed based on the principle of superposition, it was not possible to directly extend the algorithm to non-linear systems. Instead, some generalized response was defined. Then credibility of the ARMA models in predicting the generalized response was verified. Based on this credibility, the algorithm was extended for non-linear MDOF structures. Also in phase II, the stability of a controlled MDOF structure was proved. Both internal and external stability of the system were described and verified. In phase III, some problems of special interest, i.e. soil-structure interaction and control time delay, were investigated and compensated for in the framework of the developed predictive optimal control. In first part of phase III soil-structure interaction was studied. The half-space solution of the SSI effect leads to a frequency dependent representation of the structure-footing system, which is not fit for control purpose. Consequently an equivalent frequency independent system was proposed and defined as a system whose frequency response is equal to the original structure -footing system in the mean squares sense. This equivalent frequency independent system then was used in the control algorithm. In the second part of this phase, an analytical approach was used to tackle the time delay phenomenon in the context of the predictive algorithm described in previous chapters. A generalized performance index was defined considering time delay. Minimization of the generalized performance index resulted into a modified version of the algorithm in which time delay is compensated explicitly. Unlike the time delay compensation technique used in the previous phases of this investigation, which restricts time delay to be an integer multiplier of the sampling period, the modified algorithm allows time delay to be any non-negative number. However, the two approaches produce the same results if time delay is an integer multiplier of the sampling period. For evaluating the proposed algorithm and comparing it with other algorithms, several numerical simulations were carried during the research by using MATLAB and its toolboxes. A few interesting results of these simulations are enumerated below: ARM A models are able to predict the response of both linear and non-linear structures to random inputs such as earthquakes. The proposed predictive optimal control based on ARMA models has produced better results in the context of reducing velocity, displacement, total energy and operational cost compared to classic optimal control. Proposed active control algorithm is very effective in increasing safety and comfort. Its performance is not affected much by errors in the estimation of system parameters (e.g. damping). The effect of soil-structure interaction on the response to control force is considerable. Ignoring SSI will cause a significant change in the magnitude of the frequency response and a shift in the frequencies of the maximum response (resonant frequencies). Compensating the time delay effect by the modified version of the proposed algorithm will improve the performance of the control system in achieving the control goal and reduction of the structural response.

Uncertainty involved in the safe and comfort design of the structures is a major concern of civil engineers. Traditionally, the uncertainty has been overcome by utilizing various and relatively large safety factors for loads and structural properties. As a result in conventional design of for example tall buildings, the designed structural elements have unnecessary dimensions that sometimes are more than double of the ones needed to resist normal loads. On the other hand the requirements for strength and safety and comfort can be conflicting. Consequently, an alternative approach for design of the structures may be of great interest in design of safe and comfort structures that also offers economical advantages. Recently, there has been growing interest among the researchers in the concept of structural control as an alternative or complementary approach to the existing approaches of structural design. A few buildings have been designed and built based on this concept. The concept is to utilize a device for applying a force (known as control force) to encounter the effects of disturbing forces like earthquake force. However, the concept still has not found its rightful place among the practical engineers and more research is needed on the subject. One of the main problems in structural control is to find a proper algorithm for determining the optimum control force that should be applied to the structure. The investigation reported in this thesis is concerned with the application of active control to civil engineering structures. From the literature on control theory. (Particularly literature on the control of civil engineering structures) problems faced in application of control theory were identified and classified into two categories: 1) problems common to control of all dynamical systems, and 2) problems which are specially important in control of civil engineering structures. It was concluded that while many control algorithms are suitable for control of dynamical systems, considering the special problems in controlling civil structures and considering the unique future of structural control, many otherwise useful control algorithms face practical problems in application to civil structures. Consequently a set of criteria were set for judging the suitability of the control algorithms for use in control of civil engineering structures. Various types of existing control algorithms were investigated and finally it was concluded that predictive optimal control algorithms possess good characteristics for purpose of control of civil engineering structures. Among predictive control algorithms, those that use ARMA stochastic models for predicting the ground acceleration are better fitted to the structural control environment because all the past measured excitation is used to estimate the trends of the excitation for making qualified guesses about its coming values. However, existing ARMA based predictive algorithms are devised specially for earthquake and require on-line measurement of the external disturbing load which is not possible for dynamic loads like wind or blast. So, the algorithms are not suitable for tall buildings that experience both earthquake and wind loads during their life. Consequently, it was decided to establish a new closed loop predictive optimal control based on ARMA models as the first phase of the study. In this phase it was initially established that ARMA models are capable of predicting response of a linear SDOF system to the earthquake excitation a few steps ahead. The results of the predictions encouraged a search for finding a new closed loop optimal predictive control algorithm for linear SDOF structures based on prediction of the response by ARMA models. The second part of phase I, was devoted to developing and testing the proposed algorithm The new developed algorithm is different from other ARMA based optimal controls since it uses ARMA models for prediction of the structure response while existing algorithms predict the input excitation. Modeling the structure response as an AR or ARMA stochastic process is an effective mean for prediction of the structure response while avoiding measurement of the input excitation. ARMA models used in the algorithm enables it to avoid or reduce the time delay effect by predicting the structure response a few steps ahead. Being a closed loop control, the algorithm is suitable for all structural control conditions and can be used in a single control mechanism for vibration control of tall buildings against wind, earthquake or other random dynamic loads. Consequently the standby time is less than that for existing ARMA based algorithms devised only for earthquakes. This makes the control mechanism more reliable. The proposed algorithm utilizes and combines two different mathematical models. First model is an ARMA model representing the environment and the structure as a single system subjected to the unknown random excitation and the second model is a linear SDOF system which represents the structure subjected to a known past history of the applied control force only. The principle of superposition is then used to combine the results of these two models to predict the total response of the structure as a function of the control force. By using the predicted responses, the minimization of the performance index with respect to the control force is carried out for finding the optimal control force. As phase II, the proposed predictive control algorithm was extended to structures that are more complicated than linear SDOF structures. Initially, the algorithm was extended to linear MDOF structures. Although, the development of the algorithm for MDOF structures was relatively straightforward, during testing of the algorithm, it was found that prediction of the response by ARMA models can not be done as was done for SDOF case. In the SDOF case each of the two components of the state vector (i.e. displacement and velocity) was treated separately as an ARMA stochastic process. However, applying the same approach to each component of the state vector of a MDOF structure did not yield satisfactory results in prediction of the response. Considering the whole state vector as a multi-variable ARMA stochastic vector process yielded the desired results in predicting the response a few steps ahead. In the second part of this phase, the algorithm was extended to non-linear MDOF structures. Since the algorithm had been developed based on the principle of superposition, it was not possible to directly extend the algorithm to non-linear systems. Instead, some generalized response was defined. Then credibility of the ARMA models in predicting the generalized response was verified. Based on this credibility, the algorithm was extended for non-linear MDOF structures. Also in phase II, the stability of a controlled MDOF structure was proved. Both internal and external stability of the system were described and verified. In phase III, some problems of special interest, i.e. soil-structure interaction and control time delay, were investigated and compensated for in the framework of the developed predictive optimal control. In first part of phase III soil-structure interaction was studied. The half-space solution of the SSI effect leads to a frequency dependent representation of the structure-footing system, which is not fit for control purpose. Consequently an equivalent frequency independent system was proposed and defined as a system whose frequency response is equal to the original structure -footing system in the mean squares sense. This equivalent frequency independent system then was used in the control algorithm. In the second part of this phase, an analytical approach was used to tackle the time delay phenomenon in the context of the predictive algorithm described in previous chapters. A generalized performance index was defined considering time delay. Minimization of the generalized performance index resulted into a modified version of the algorithm in which time delay is compensated explicitly. Unlike the time delay compensation technique used in the previous phases of this investigation, which restricts time delay to be an integer multiplier of the sampling period, the modified algorithm allows time delay to be any non-negative number. However, the two approaches produce the same results if time delay is an integer multiplier of the sampling period. For evaluating the proposed algorithm and comparing it with other algorithms, several numerical simulations were carried during the research by using MATLAB and its toolboxes. A few interesting results of these simulations are enumerated below: ARM A models are able to predict the response of both linear and non-linear structures to random inputs such as earthquakes. The proposed predictive optimal control based on ARMA models has produced better results in the context of reducing velocity, displacement, total energy and operational cost compared to classic optimal control. Proposed active control algorithm is very effective in increasing safety and comfort. Its performance is not affected much by errors in the estimation of system parameters (e.g. damping). The effect of soil-structure interaction on the response to control force is considerable. Ignoring SSI will cause a significant change in the magnitude of the frequency response and a shift in the frequencies of the maximum response (resonant frequencies). Compensating the time delay effect by the modified version of the proposed algorithm will improve the performance of the control system in achieving the control goal and reduction of the structural response.

Thesis (PhD)--University of Stellenbosch, 2002.
ENGLISH ABSTRACT: Structural analysis is examined in order to identify its essential information requirements, its fundamental tasks, and the essential functionalities that applications which support it should provide. The special characteristics of the information content of structural analysis and the algorithms that operate on it are looked into and exploited to devise data structures and utilities that provide proper support of the analysis task within a local environment, while presenting the opportunity to be extended to the context of a distributed network-based collaboratory as well. Aspects regarding the distribution of analysis parameters and methods are analysed and alternatives are evaluated. The extentions required to adapt the local data structures and utilities for use in a distributed communication network are developed and implemented in pilot form. Examples of collaborative analysis are shown, and an evaluation of the overhead involved in distributed work is performed.
AFRIKAANSE OPSOMMING: 'n Ondersoek van die struktuuranalise-taak word uitgevoer waarin die kerninligtingsbehoeftes en fundamentele take daarvan, asook die vereisde funksionaliteit van toepassings wat dit ondersteun bepaal word. Die besondere eienskappe van struktuuranalise-inligting en die algoritmes wat daarop inwerk word ondersoek en benut om data strukture en metodes te ontwikkel wat die analise-taak goed ondersteun in In lokale omgewing, en wat terselfdertyd die moontlikheid bied om sodanig uitgebrei te word dat dit ook die taak in 'n verspreide samewerkingsgroepering kan ondersteun. Aspekte van die verspreiding van analiseparameters en metodes word ondersoek en alternatiewe oplossings word evalueer. Die uitbreidings wat nodig is om die datastrukture en metodes van die lokale omgewing aan te pas vir gebruik in verspreide kommunikasienetwerke word ontwikkel en in loodsvorm toegepas. Voorbeelde van samewerking-gebasseerde analise word getoon, en die oorhoofse koste verbonde aan analise in 'n verdeelde omgewing word evalueer.

Nowadays, standard “Performance Based Seismic Design” (PBSD) procedures rely on a “Probabilistic Seismic Hazard Analysis” (PSHA) to define the seismic input. Many assumptions underlying the probabilistic method have been proven wrong. Many earthquakes, not least the Italian earthquake sequence of 2016 (still in progress), have shown the limits of a PBSD procedure based on PSHA. Therefore, a different method to define the seismic hazard should be defined and used in a PBSD framework. This thesis tackles this aspect. In the first chapter a review of the standard PBSD procedures is done, focusing on the link between the seismic input and the acceptable structural performance level for a building. It is highlighted how, at least when evaluating the Collapse Prevention Level (CP), the use of a probabilistic seismic input should be avoided. Instead, the concept of “Maximum Credible Seismic Input” (MCSI) is introduced. This input should supply Maximum Credible Earthquake (MCE) level scenario ground motions, in other words an “upper bound” to possible future earthquake scenarios. In the second chapter an upgrade of the “Neo Deterministic Seismic Hazard Assessment” (NDSHA) is proposed to compute NDSHA-MCSI, henceforth shortly called MCSI. In other words, MCSI is fully bolted to NDSHA and aims to define a reliable and effective design seismic input. NDSHA is a physics-based approach where the ground motion parameters of interest (e.g. PGA, SA, SD etc.) are derived from the computation of thousands of physics-based synthetic seismograms calculated as the tensor product between the tensor representing in a formal way the earthquake source and the Green’s function of the medium. NDSHA accommodates the complexity of the source process, as well as site and topographical effects. The comparison between the MCSI response spectra, the Italian Building Code response spectra and the response spectra of the three strongest events of the 2016 central Italy seismic sequence is discussed. Exploiting the detailed site-specific mechanical conditions around the recording station available in literature, the methodology to define MCSI is applied to the town of Norcia (about five km from the strongest event). The results of the experiment confirm the inadequacy of the probabilistic approach that strongly underestimated the spectral accelerations for all three events. On the contrary, MCSI supplies spectral accelerations well comparable with those generated by the strongest event and confirms the reliability of the NDSHA methodology, as happened in previous earthquakes (e.g. Aquila 2009 and Emilia 2012). In the third chapter a review of the PBSD is done. It emphasizes the arbitrariness with which different choices, at present taken for granted all around the world, were taken. A new PBSD framework based on the use of MCSI is then proposed. This procedure is independent from the arbitrary choice of the reference life and the probability of exceedance. From an engineering point of view, seismograms provided by NDSHA simulations also allow to run time history analysis using site specific inputs even where no records are available. This aspect is evidenced in chapter four where a comparison between some Engineering Demand Parameters (EDP) on a steel moment resisting frame due to natural and synthetic accelerograms are compared. This thesis shows that, at least when assessing the CP level, the use of PSHA in a PBSD approach should be avoided. The new PBSD framework proposed in thesis and based on MCSI computation, if used, could help to prevent collapse of buildings and human losses, hence to build seismic resilient systems and to overcome the limits of probabilistic approaches. Not least, the availability of site specific accelerograms could lead to wider use of Non-Linear Time History Analysis (NLTHA), therefore to a better understanding of the seismic behaviour of structures.
Nowadays, standard “Performance Based Seismic Design” (PBSD) procedures rely on a “Probabilistic Seismic Hazard Analysis” (PSHA) to define the seismic input. Many assumptions underlying the probabilistic method have been proven wrong. Many earthquakes, not least the Italian earthquake sequence of 2016 (still in progress), have shown the limits of a PBSD procedure based on PSHA. Therefore, a different method to define the seismic hazard should be defined and used in a PBSD framework. This thesis tackles this aspect. In the first chapter a review of the standard PBSD procedures is done, focusing on the link between the seismic input and the acceptable structural performance level for a building. It is highlighted how, at least when evaluating the Collapse Prevention Level (CP), the use of a probabilistic seismic input should be avoided. Instead, the concept of “Maximum Design Seismic Input” (MDSI) is introduced. This input should supply Maximum Credible Earthquake (MCE) level scenario ground motions, in other words an “upper bound” to possible future earthquake scenarios. In the second chapter an upgrade of the “Neo Deterministic Seismic Hazard Assessment” (NDSHA) is proposed to find MDSI, henceforth called NDSHA-MDSI. NDSHA is a physics-based approach where the ground motion parameters of interest (e.g. PGA, SA, SD etc.) are derived from the computation of thousands of physics-based synthetic seismograms calculated as the tensor product between the tensor representing in a formal way the earthquake source and the Green’s function of the medium. NDSHA accommodates the complexity of the source process, as well as site and topographical effects. The comparison between the NDSHA-MDSI response spectra, the Italian Building Code response spectra and the response spectra of the three strongest events of the 2016 central Italy seismic sequence is discussed. Exploiting the detailed site-specific mechanical conditions around the recording station available in literature, the methodology to define NDSHA-MDSI is applied to the town of Norcia (about five km from the strongest event). The results of the experiment confirm the inadequacy of the probabilistic approach that strongly underestimated the spectral accelerations for all three events. On the contrary, NDSHA-MDSI supplies spectral accelerations well comparable with those generated by the strongest event and confirms the reliability of the NDSHA methodology, as happened in previous earthquakes (e.g. Aquila 2009 and Emilia 2012). In the third chapter a review of the PBSD is done. It emphasizes the arbitrariness with which different choices, at present taken for granted all around the world, were taken. A new PBSD framework based on the use of MDSI is then proposed. This procedure is independent from the arbitrary choice of the reference life and the probability of exceedance. From an engineering point of view, seismograms provided by NDSHA simulations also allow to run time history analysis using site specific inputs even where no records are available. This aspect is evidenced in chapter four where a comparison between some Engineering Demand Parameters (EDP) on a steel moment resisting frame due to natural and synthetic accelerograms are compared. This thesis shows that, at least when assessing the CP level, the use of PSHA in a PBSD approach should be avoided. The new PBSD framework proposed in thesis and based on NDSHA-MDSI computation, if used, could help to prevent collapse of buildings and human losses hence to build seismic resilient systems and to overcome the limits of probabilistic approaches. Not least, the availability of site specific accelerograms could lead to wider use of Non-Linear Time History Analysis (NLTHA) hence to a better understanding of the seismic behaviour of structures.

Computer-aided structural analysis processes are highly dependent on the use of computer graphics. The objective of this work is to evolve techniques that allow structural analysts, designers and architects to work with computer graphics in a convenient manner. The formex approach of data generation is explained through a number of examples. This approach enables data to be generated very conveniently for the purposes of structural analysis. Also, introduced are the main features of an interactive programming language which acts as a vehicle to implement the concepts of formex algebra. An attempt to investigate the possibility of using the concepts of formex graphics in postprocessing stages of structural analysis is presented. This enables output of structural analysis programs to be graphically displayed so that plots of structural configurations can be shown in both their deformed and undeformed shapes. It is also shown that it is possible to employ the concepts of formex graphics in order to produce axial force, shear force, bending moment and torque diagrams in a manner that they can be visualized conveniently.

Aspendos Theatre still stands in fairly good condition although it has been constructed about 2200 years ago in Serik village of Antalya, Turkey. Aspendos Theatre is one of the most valuable historical buildings in Turkey. The fact that the structure had overcome numerous possible earthquakes during its lifespan in Antalya and located in second degree earthquake zone, makes the subject an interesting research topic. The earthquake analysis of Aspendos Theatre was conducted using Specification for Structures to be Built in Disaster Areas code and stress levels are investigated using 3D FE modeling. Also, the resonance state of the theatre under sound induced forces due to concerts and exhibitions performed in the theatre has been examined. Structural identification is performed to obtain certain structural characteristics by comparing experimentally measured and analytically obtained natural frequencies. The analytical model is constructed using solid members and the analysis is performed by using SAP2000 software. The elastic modulus of conglomerate used as building blocks in the Theatre is taken as 2350 MPa based on the experimental and analytical studies. The compressive and tensile strength of the theatre wall material is taken as 12 MPa and 1.2 MPa, respectively based on the previous studies conducted on conglomerate. When the maximum stress levels under combined effect of response spectrum and dead load analyses are examined, the level of compressive stress is found to be about 60% of the compressive strength. On the other hand, the tensile stresses developing at upper corners and bottom middle parts of the stage wall and mid-height central location of the exterior wall (on the vicinity of the front door) are calculated to be about 6.6 MPa, which are more than the assumed tensile strength. It has also been calculated that the level of sound that generates tensile failure is about 125 dB as the theatre gets into resonance state.

The focus of this work is to advance the theoretical and modeling techniques for the fields of hybrid simulation and multi-slider friction pendulum systems (MSFPs). Hybrid Simulation is a simulation technique involving the integration of a physical system and a computational system with the use of actuators and sensors. This method has a strong foundation in the experimental mechanics community where it has been used for many years. The hybrid simulation experiments are performed with the assumption of an accurate result as long as the main causes of error are reduced. However, the theoretical background on hybrid testing needs to be developed in order validate these findings using this technique. To achieve this objective, a model for hybrid simulation is developed and applied to three test cases: an Euler-Bernoulli beam, a nonlinear damped, driven pendulum, and a boom crane structure. Due to the complex dynamics that these three test cases exhibit, L² norms, Lyapunov exponents, and Lyapunov dimensions, as well as correlation exponents were utilized to analyze the error in hybrid simulation tests. From these three test cases it was found that hybrid simulations are highly dependent on the natural frequencies of the dynamical system as well as how and where the hybrid split is located. Thus, proper care must be taken when conducting a hybrid experiment in order to guarantee reliable results.

Multi-stage friction pendulum systems (MSFPs), such as the triple friction pendulum (TFP), are currently being developed as seismic isolators. However, all current analytical models are inadequate in modeling many facets of these devices. Either the model can only handle uni-directional ground motions while incorporating the kinetics of the TFP system, or the model ignores the kinetics and can handle bi-directional motion. And in all cases, the model is linearized to simplify the equations. The second part of this dissertation presents an all-in-one model that incorporates the full nonlinear kinetics of the TFP system, while allowing for bi-directional ground motion. In this way, the model presented here is the most complete single model currently available. It was found that the non-linear model can more accurately predict the experimental results for large displacements due to the nonlinear kinematics used to describe the system. The model is also able to successfully predict the experimental results for bi-directional ground motions.

Bibliography: p. 113-123.
This thesis investigates probabilistic and stochastic methods for structural analysis which can be integrated into existing, commercially available finite element programs. It develops general probabilistic finite element routines which can be implemented within deterministic finite element programs without requiring major code development. These routines are implemented in the general purpose finite element program ABAQUS through its user element subroutine facility and two probabilistic finite elements are developed: a three-dimensional beam element limited to linear material behaviour and a two-dimensional plane element involving elastic-plastic material behaviour. The plane element incorporates plane strain, plane stress and axisymmetric formulations. The numerical accuracy and robustness of the routines are verified and application of the probabilistic finite element method is illustrated in two case studies, one involving a four-story, two-bay frame structure, the other a reactor pressure vessel nozzle. The probabilistic finite element routines developed in this thesis integrate point estimate methods and mean value first order methods within the same program. Both methods require a systematic sequence involving the perturbation of the random parameters to be evaluated, although the perturbation sequence of the methods differ. It is shown that computer-time saving techniques such as Taylor series and iterative perturbation schemes, developed for mean value based methods, can also be used to solve point estimate method problems. These efficient techniques are limited to linear problems; nonlinear problems must use full perturbation schemes. Finally, it is shown that all these probabilistic methods and perturbation schemes can be integrated within one program and can follow many of the existing deterministic program structures and subroutines. An overall strategy for converting deterministic finite element programs to probabilistic finite element programs is outlined.

This thesis investigated the application of seismic analysis methods and the response of idealized shear frames subjected to seismic loading. To complete this research, a Design Basis Earthquake (DBE) for a project site in San Luis Obispo, CA, and five past earthquake records were considered. The DBE was produced per the American Society of Civil Engineers’ Minimum Design Loads for Buildings and Other Structures (ASCE 7-10) and used for application of the Equivalent Lateral Force Procedure (ELFP) and Response Spectrum Analysis (RSA). When applying RSA, the modal peak responses were combined using the Absolute Sum (ABS), Square-Root-of-the-Sum-of-Squares (SRSS), and Complete Quadratic Combination (CQC) method. MATLAB scripts were developed to produce several displacement, velocity, and acceleration spectrums for each earthquake. Moreover, MATLAB scripts were written to yield both analytical and numerical solutions for each system through application of Linear Time History Analysis (THA). To obtain analytical solutions, two implicit forms of the Newmark-beta Method were employed: the Average Acceleration Method and the Linear Acceleration Method. To generate a comparison, the ELFP, RSA, and THA methods were applied to shear frames up to ten stories in height. The system parameters that impacted the accuracy of each method and the response of the systems were analyzed, including the effects of classical damping and nonclassical damping models. In addition to varying levels of Rayleigh damping, non-linear hysteric friction spring dampers (FSDs) were implemented into the systems. The design of the FSDs was based on target stiffness values, which were defined as portions of the system’s lateral stiffness. To perform the required Nonlinear Time History Analysis (NTHA), a SAP2000 model was developed. The efficiencies of the FSDs at each target stiffness, with and without the addition of low levels of viscous modal damping are analyzed. It was concluded that the ELFP should be supplemented by RSA when performing seismic response analysis. Regardless of system parameters, the ELFP yielded system responses 30% to 50% higher than RSA when combing responses with the SRSS or CQC method. When applying RSA, the ABS method produced inconsistent and inaccurate results, whereas the SRSS and CQC results were similar for regular, symmetric systems. Generally, the SRSS and CQC results were within 5% of the analytical solution yielded through THA. On the contrary, for irregular structures, the SRSS method significantly underestimated the response, and the CQC method was four to five times more accurate. Additionally, both the Average Acceleration Method and Linear Acceleration Method yielded numerical solutions with errors typically below 1% when compared with the analytical solution. When implemented into the systems, the FSDs proved to be most efficient when designed to have stiffnesses that were 50% of the lateral stiffness of each story. The addition of 1% modal damping to the FSDs resulted in quicker energy dissipation without significantly reducing the peak response of the system. At a stiffness of 50%, the FSDs reduced the displacement response by 40% to 60% when compared with 5% modal damping. Additionally, the FSDs at low stiffnesses exhibited the effects of negative lateral stiffness due to P-delta effects when the earthquake ground motions were too weak to induce sliding in the ring assemblies.

This thesis focuses on the structural behavior of a washer machine cylinder. The cylinder is the component in the washing machine that rotates and keeps the laundry in place. The aim of this thesis is to determine the maximum load applied to the cylinder at which crack propagation occurs. Three experiments are performed to determine the structural behavior of the cylinder. Two experiments are performed to estimate mechanical properties i.e. stress-strain relation and critical fracture energy of the stainless steel sheet in use today. This is to derive a good estimation of the maximum load the cylinder can endure. The third type of experiment is performed to determine the strains on the outer surface of the cylinder when an evenly distributed load, 11 kg, and 2200 revolution per minute are applied on the inner surface of the cylinder. Three numerical models are performed from these three types of experiments which gives an estimation of the work to be done to propagate the crack at 15 kg and 2400 rpm. The question is if this load is overestimated to start crack propagation? This load is considerably higher than the washer machines operating speed.

This thesis examines the fatigue behaviour of FPSO structures. It has been compiled as a result of theoretical, analytical and experimental study. The Finite Element approach has been utilized to analyse the FPSO's structure. It is intended that this particular work will enable further computer simulations for fatigue assessment to be carried out. The thesis starts with the development of the general arrangement, structure and typical details of the City FPSO. The applied loads are then reviewed and this includes the so called static loads due to cargo loading and still water pressure, and the green loads due to dynamic loads induced by the vessel behaviour on waves at sea. Response to local loads such as, external sea pressure, internal pressure due to the cargo and ballast, wave slamming loads, etc. is then determined. The effect of the top structural loads on the FPSO is discussed with some practical calculation of typical topside processing palates loads. SCF evaluation methods are considered together with a discussion of the effect of structural dimensioning of local details, the use of specially performed test results conducted on ship structure. In particular, the structural stress concentration factor at the web-toe associated with the max loading conditions is developed. Confirmation of validity of the SCFs theory is provided from an extensive appraisal of the literature and from laboratory tests of the structure in question. The experimental technique developed in this thesis is based upon geometrical analogy to the simplified Peterson's Neuber notch theory, applied to the system parametric equations of SCFs and the geometric relations. The experimental results are in general accordance with published results. This research includes a calibration method for S-N Curves required for typical fatigue sensitive details in FPSOs. It also provides improved information on the important link between S-N data and finite element analysis for fatigue life assessment using a linear cumulative damage formulation.

In order to be able to undertake an analysis of a component the designer will need to know the properties of the material being used. The aim of this work is help the design engineer such that the mechanical properties of continuous glass fibre reinforced composite material can be determined and used in the design analysis of components manufactured from this material. The literature survey has shown that for the material considered here, then given the constituent properties, the fibre arrangement and the fibre volume fraction, the composite mechanical properties may be determined mathematically by the use of micromechanical equations. The micromechanical prediction of the mechanical properties of uni-directional, random and woven fibre reinforced composites has been examined. The variation of these mechanical properties that may occur in a composite component due to the manufacturing process has been highlighted as being of importance. This has been studied to determine whether such a variation is significant by analysing examples of composite components and plates. The results from these analyses have been correlated with experimental results and investigated to study the importance of such variations in properties. Many micromechanical equations have been found in the literature for the prediction of the mechanical properties of continuous fibre reinforced composite materials. An accuracy of the predicted properties to within 10% of the experimental data was concluded to be acceptable and good enough for initial design purposes as design engineers are not usually able to design to such tight tolerances. This work has shown that further development of the micromechanical theories is not the most important problem concerning the prediction of the mechanical properties. These properties can currently be predicted with acceptable accuracy from the micromechanical equations already available in the literature. However, the design engineer is unlikely to have knowledge of the micromechanical equations necessary to determine the required properties. It is only by undertaking a large literature survey that the designer would be able to find this information. Many of the micromechanical equations require the use of an empirical factor. The knowledge of a value for such a factor is again something that would not be readily available to the designer. Rather than concentrating upon improving the micromechanical predictions, this work shows that effort should be made to understand the influence of other factors upon the mechanical properties of composite materials. In particular, the behaviour and flow of the material during the manufacturing process has been highlighted as being of importance as it can cause a significant variation in the properties. Thus, analyses of composite components cannot assume that the mechanical properties are constant throughout, and it is therefore necessary to first model the manufacturing process to determine the mechanical properties before undertaking a structural analysis.

Seismic events around the globe directly affect all ranges of structures, from complex and expensive ‘skyscrapers’ to simple frame structures, the latter making up a higher proportion of the number of structures affected as they are a much more common type of structure. The impact of a seismic event can be devastating, especially if adequate predictions of their impact and imposed structural response are not made during the design stage of the structure. Knowing what response to expect allows the engineer to design the structure to survive an event and protect the occupants. The structural response to a seismic event is very complex and can be affected by a wide range of structural, geotechnical and environ parameters. While larger, expensive structures make use of expensive, time consuming, finite element analytical procedures to determine their response the cheaper, simpler, frame structures have to make do with existing, simplified, spectral method predictions. This research firstly involves finite element analysis of simple frame structures, considering different structural and geotechnical parameters which may influence the seismic response, namely the stiffness of the structural joints, the geometry of the structure (influencing the individual structural element flexibility) and the foundation conditions (fixed base or shallow foundations with soil structure interaction). A range of frames, of varying geometry, are considered which mobilise different amounts of inter-storey drift, local rotation and global rotation response. The influence of soil structure interaction (SSI) and frame rigidity (i.e. the properties of the joints) on the response behaviour is investigated. The finite element database is then used to validate improved methods for predicting the spectral response parameters, specifically the natural period and damping of equivalent single degree of freedom (SDOF) systems, which include the effects of frame rigidity, geometry and SSI. Dynamic centrifuge testing is also carried out in order to further validate the improved spectral model for the case of real soil with shear dependant stiffness. The physical model testing is also extended to consider how environs, such as other structures in close proximity, influence the response of a structure.

A simulation-based reliability analysis method is presented and evaluated. This method is intended for problems for which most probable point of failure (MPP) search-based methods fail or provide inaccurate results, and for which Monte Carlo simulation and its variants are too costly to apply. This may occur in the evaluation of complex engineering problems of low failure probability. The method used to address this problem is a variant of conditional expectation and works by sampling on the failure boundary without relying on the MPP. The effectiveness of the method is compared to a selection of other commonly available reliability methods considering a variety of analytical as well as more complex engineering problems. The results indicate that the method has the potential to deliver solutions of high efficiency and accuracy for a wide range of difficult reliability problems.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 935-1001).
Structural failures of bulk carriers continue to account for the loss of many lives every year. Capes are particularly vulnerable to cracking because of their large length, their trade in high density cargos, and the high rates of cargo operations. Rapid loss often occurs allowing little reaction time which has alarmed the industry. The Cape market is extremely volatile with ship values appreciating in some cases by over 500% and then returning to original levels, all within a few years. Recent market changes have rendered conventional pricing methods inaccurate and often inapplicable, resulting in a pressing need for alternate valuation models. Very little research combines the closely interlinked technical and financial elements which are crucial for valuation and decision making by various parties in the shipping industry. The present research involves the collection and analysis of one of the largest ship cracking surveys. It is focused specifically on capes which lie at the core of the problem and is based on the records of ship owners, classification societies and shipyards. A location coding system was specifically designed to analyze the data and present the frequency, size and estimated crack growth rates with respect to location and ship age. The results were compared with existing knowledge based on surveys conducted over the past 50 years, the stress distribution based on an investigation of loading patterns, and theoretical fracture mechanics predictions. They were then combined with the frequency of crack failures, derived from an investigation of an extensive fleet sample, to develop a reliability model which yields the hazard function throughout the ship's life. Repair procedures and design modifications were also examined and a model was designed to assess their cost effectiveness based on the present value of projected crack costs. The crack repair costs were calculated as a function of ship age to be used in conjunction with the safety assessment for decision making by ship owners, insurance companies, classification societies and others. A new state of the art valuation model was developed combining both technical and financial aspects in a fundamental valuation based on risk-adjusted discounting of expected cash flows. A forward view of the main parameters was obtained from derivatives and financial securities that include shipping futures, FFAs, options, interest rate swaps and inflation protected bonds. The inherent risk of cracks is treated as a fictitious credit risk, derived from the reliability model, and is incorporated into the discount rate along with other risk premiums. Other inputs include repair costs and off-hire time, which were calculated with respect to ship age using a database of repairs, while the records of public and private companies were used along with surveys to estimate operating expenses. The resulting valuations were found to be in very close alignment with recent transaction prices across all ship ages. The model also estimates the volatility of the ship value and uses it to price optionalities that are often included in ship transactions. The combination of technical and financial analysis of this thesis is valuable to many involved in the shipping industry including brokers, accountants, analysts, shipping banks and investors interested in valuation; ship owners when making managerial or investment decisions; shipyards when designing ships, setting prices and deciding payment structures and options; insurance companies when covering total loss or emergency repairs; the IMO when setting regulations; and classification societies when scheduling inspections and deciding which areas to focus on.
by Nicholas Andrew Hadjiyiannis.
Ph.D.

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2009.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 23).
Although cost effective and environmentally friendly, bicycles are impractical for many users due to the required strength and physical exertion. The GreenWheel is a set of mechanical and electronic devices that provide adjustable amounts of torque to a bicycle wheel to assist the rider in pedaling. This device makes bicycles accessible to a much larger fraction of the population. The device consists of two main modules, one of which is mounted on the handlebar, allowing the user a convenient way to set a desired torque output. It functions to wirelessly convey this information to the second main module, which mounts at the center of the rear wheel of the bicycle and is designed to exert a user-desired amount of torque to the wheel. The inner portion of this module contains a motor layout, including batteries, solenoids, and magnets. The outer portion of this module is a casing that rotates on bearings on the bicycle shaft. It is held in place by the spokes of the wheel that attach to the holes at the circumference of the device. Originally the device was designed to operate using brushed DC motors. Realizing the potential of brushless DC motors, brushed DC motors were abandoned in the design of the actual product that will be released in the market. This change required a complete redesign of the inner casing that stored the motor. This also created the need to redesign the outer casing to provide the device with the proper structural integrity and a more appealing and elegant design. This thesis focuses on the redesign of the outer casing, the analysis of its two critical components, and its aesthetics. One of its two critical components is the material of spoke-holes on the circumference of the outer casing to which the spokes will be attached. It was evaluated for the amount of shear that it will experience as a result of spoke tension. The second critical component is the material of the bicycle shaft to which the motor was attached. It was analyzed to prevent failure from shearing due to the electromagnetic forces created by the motor coils. In addition, aesthetics and ease of assembly and servicing were also considered in the design of the device. The area of the outer casing that surrounds the spoke-holes was analyzed using the largest amount of force that it will experience from the spokes. It was found that these areas that surround the spoke-holes are strong enough to withstand the shear stress from the spokes. The shaft was designed to withstand the torsion generated during the operation of the motor.
by Kashika Sharma.
S.B.

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2011.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 26).
It is useful for one owning or buying a house to be able to assess its structure and identify the existence and severity of any damage. No previously existing method appears to make this assessment easily available. This thesis predicts that architecture will fail in some combination of eleven predictable ways that a simple robot can observe and distinguish by measuring the slope of select points on the floor. This prediction was tested on a case study house, and the model predicted 78.7% of the observed contour. A compact robot was fabricated and measurements of inclination were compared with those of a standard digital inclinometer. The ratio of the angle measured with the robot to that measured with the inclinometer was found to be 1.034 ± 0.193. This proof-of-concept study indicates that an inexpensive robot could be developed as a commercial product capable of assessing the structural safety of common houses.
by Noah S. Caplan.
S.B.

Abnormal vascular structure has been identified as one of the major characteristics of tumours. In this thesis, we carry out quantitative analysis on different tumour vascular structures and research the relationship between vascular structure and its transportation efficiency. We first study segmentation methods to extract the binary vessel representations from microscope images. We found that local phase-hysteresis thresholding is able to segment vessel objects from noisy microscope images. We also study methods to extract the centre lines of segmented vessel objects, a process termed as skeletonization. We modified the conventional thinning method to regularize the extremely asymmetrical structure found in the segmented vessel objects. We found this method is capable to produce vessel skeletons with satisfactory accuracy. We have developed a software for 3D vessel structural analysis. This software is consisted of four major parts: image segmentation, vessel skeletonization, skeleton modification and structure quantification. This software has implemented local phase-hysteresis thresholding and structure regularization-thinning methods. A GUI was introduced to enable users to alter the skeleton structures based on their subjective judgements. Radius and inter branch length quantification can be conducted based on the segmentation and skeletonization results. The accuracy of segmentation, skeletonization and quantification methods have been tested on several synthesized data sets. The change of tumour vascular structure after drug treatment was then investigated. We proposed metrics to quantify tumour vascular geometry and statistically analysed the effect of tested drugs on normalizing tumour vascular structure. finally, we developed a spatio-temporal model to simulate the delivery of oxygen and 3-18 F-fluoro-1-(2-nitro-1-imidazolyl)-2-propanol (Fmiso), which is the hypoxia tracer that gives out PET signal in an Fmiso PET scanning. This model is based on compartmental models, but also considers the spatial diffusion of oxygen and Fmiso. We validated our model on in vitro spheroid data and simulated the oxygen and Fmiso distribution on the segmented vessel images. We contend that the tumour Fmiso distribution (as observed in Fmiso PET imaging) is caused by the abnormal tumour vascular structure which is further aroused from tumour angiogenesis process. We depicted a modelling framework to research the relationships between tumour angiogenesis, vessel structure and Fmiso distribution, which is going to be the focus of our future work.

Includes bibliographical references.
This dissertation covers the application of finite element analysis and hull stress monitoring and measuring methods, in the current day design of, and/or the analysis of ship structures.

碩士
國立海洋大學
造船工程學系
82
Computer has been used for years in the field of structure analysis. However ,only individual program is used for each different step in the whole procedure of analysis work. In this project , the concept of concurrent engineering is used in the computer aided structure analysis. Integration of the generation of structure model, creation of finite element mesh ,analysis and studies of the results and futhermore to the modification of the model with reanalysis works are studied thoroughly. The whole process is executed under the Windows system on a personal computer which is useful for the improvement of the efficiency of computer aided structure analysis.

Probabilistic methods have been widely used in structural engineering to model uncertainties in loads and structural properties. The subjects of structural reliability analysis, random vibrations, and structural system identification have been extensively developed and provide the basic framework for developing rational design and maintenance procedures for engineering structures. One of the crucial requirements for successful application of probabilistic methods in these contexts is that one must have access to adequate amount of empirical data to form acceptable probabilistic models for the uncertain variables. When this requirement is not met, it becomes necessary to explore alternative methods for uncertainty modeling. Such efforts have indeed been made in structural engineering, albeit to a much lesser extent as compared to efforts expended in developing probabilistic methods. The alternative frameworks for uncertainty modeling include methods based on the use of interval analysis, convex function representations, theory of fuzzy variables, polymorphic models for uncertainties, and hybrid models which combine two or more of alternative modeling frameworks within the context of a given problem. The work reported in this thesis lies in the broad area of research of modeling uncertainties using non-probabilistic and combined non-probabilistic and probabilistic methods. The thesis document is organized into 5 chapters and 6 annexures. A brief overview of alternative frameworks for uncertainty modeling and their mathematical basis are provided in chapter 1. This includes discussion on modeling of uncertainties using intervals and issues related to uncertainty propagation using interval algebra; details of convex function models and relevance of optimization tools in characterizing uncertainty propagation; discussion on fuzzy variables and their relation to intervals and convex functions; and, issues arising out of treating uncertainties using combined probabilistic and non-probabilistic methods. The notion of aleatoric and epistemic uncertainties is also introduced and a brief mention of polymorphic models for uncertainty, which aim to accommodate alternative forms of uncertainty within a single mathematical model, is made. A review of literature pertaining to applications of non-probabilistic and combined probabilistic and non-probabilistic methods for uncertainty modeling in structural engineering applications is presented in chapter 2. The topics covered include: (a) solutions of simultaneous algebraic equations, eigenvalue problems, ordinary differential equations, and the extension of finite element models to include non-probabilistic uncertainties, (b) issues related to methods for arriving at uncertainty models based on empirical data, and (c) applications to problems of structural safety and structural optimization. The review identifies scope for further research into the following aspects: (a) development of methods for arriving at optimal convex function models for uncertain variables based on limited data and embedding the models thus developed into problems of structural safety assessment, and (b) treatment of inverse problems arising in structural safety based design and optimization which takes into account possible use of combined probabilistic and non-probabilistic modeling frameworks. Chapter 3 considers situations when adequate empirical data on uncertain variables is lacking thereby necessitating the use of non-probabilistic approaches to quantify uncertainties. The study discusses such situations in the context of structural safety assessment. The problem of developing convex function and fuzzy set models for uncertain variables based on limited data and subsequent application in structural safety assessment is considered. Strategies to develop convex set models for limited data based on super-ellipsoids with minimum volume and Nataf’s transformation based method are proposed. These models are shown to be fairly general (for instance, approximations to interval based models emerge as special cases). Furthermore, the proposed convex functions are mapped to a unit multi-dimensional sphere. This enables the evaluation of a unified measure of safety, defined as the shortest distance from the origin to the limit surface in the transformed standard space, akin to the notion used in defining the Hasofer- Lind reliability index. Also discussed are issues related to safety assessment when mixed uncertainty modeling approach is used. Illustrative examples include safety assessment of an inelastic frame with uncertain properties. The study reported in chapter 4 considers a few inverse problems of structural safety analysis aimed at the determination of system parameters to ensure a target level of safety and (or) to minimize a cost function for problems involving combined probabilistic and non-probabilistic uncertainty modeling. Development of load and resistance factor design format, in problems with combined uncertainty models, is also presented. We employ super-ellipsoid based convex function/fuzzy variable models for representing non-probabilistic uncertainties. The target safety levels are taken to be specified in terms of indices defined in standard space of uncertain variables involving standard normal random variables and (or) unit hyper-spheres. A class of problems amenable for exact solutions is identified and a general procedure for dealing with more general problems involving nonlinear performance functions is developed. Illustrations include studies on inelastic frame with uncertain properties. A summary of contributions made in the thesis, along with a few suggestions for future research, are presented in chapter 5. Annexure A-F contain the details of derivation of alternative forms of safety measures, Newton Raphson’s based methods for optimization used in solutions to inverse problems, and details of combining Matlab based programs for uncertainty modeling with Abaqus based models for structural analysis.

Probabilistic methods have been widely used in structural engineering to model uncertainties in loads and structural properties. The subjects of structural reliability analysis, random vibrations, and structural system identification have been extensively developed and provide the basic framework for developing rational design and maintenance procedures for engineering structures. One of the crucial requirements for successful application of probabilistic methods in these contexts is that one must have access to adequate amount of empirical data to form acceptable probabilistic models for the uncertain variables. When this requirement is not met, it becomes necessary to explore alternative methods for uncertainty modeling. Such efforts have indeed been made in structural engineering, albeit to a much lesser extent as compared to efforts expended in developing probabilistic methods. The alternative frameworks for uncertainty modeling include methods based on the use of interval analysis, convex function representations, theory of fuzzy variables, polymorphic models for uncertainties, and hybrid models which combine two or more of alternative modeling frameworks within the context of a given problem. The work reported in this thesis lies in the broad area of research of modeling uncertainties using non-probabilistic and combined non-probabilistic and probabilistic methods. The thesis document is organized into 5 chapters and 6 annexures. A brief overview of alternative frameworks for uncertainty modeling and their mathematical basis are provided in chapter 1. This includes discussion on modeling of uncertainties using intervals and issues related to uncertainty propagation using interval algebra; details of convex function models and relevance of optimization tools in characterizing uncertainty propagation; discussion on fuzzy variables and their relation to intervals and convex functions; and, issues arising out of treating uncertainties using combined probabilistic and non-probabilistic methods. The notion of aleatoric and epistemic uncertainties is also introduced and a brief mention of polymorphic models for uncertainty, which aim to accommodate alternative forms of uncertainty within a single mathematical model, is made. A review of literature pertaining to applications of non-probabilistic and combined probabilistic and non-probabilistic methods for uncertainty modeling in structural engineering applications is presented in chapter 2. The topics covered include: (a) solutions of simultaneous algebraic equations, eigenvalue problems, ordinary differential equations, and the extension of finite element models to include non-probabilistic uncertainties, (b) issues related to methods for arriving at uncertainty models based on empirical data, and (c) applications to problems of structural safety and structural optimization. The review identifies scope for further research into the following aspects: (a) development of methods for arriving at optimal convex function models for uncertain variables based on limited data and embedding the models thus developed into problems of structural safety assessment, and (b) treatment of inverse problems arising in structural safety based design and optimization which takes into account possible use of combined probabilistic and non-probabilistic modeling frameworks. Chapter 3 considers situations when adequate empirical data on uncertain variables is lacking thereby necessitating the use of non-probabilistic approaches to quantify uncertainties. The study discusses such situations in the context of structural safety assessment. The problem of developing convex function and fuzzy set models for uncertain variables based on limited data and subsequent application in structural safety assessment is considered. Strategies to develop convex set models for limited data based on super-ellipsoids with minimum volume and Nataf’s transformation based method are proposed. These models are shown to be fairly general (for instance, approximations to interval based models emerge as special cases). Furthermore, the proposed convex functions are mapped to a unit multi-dimensional sphere. This enables the evaluation of a unified measure of safety, defined as the shortest distance from the origin to the limit surface in the transformed standard space, akin to the notion used in defining the Hasofer- Lind reliability index. Also discussed are issues related to safety assessment when mixed uncertainty modeling approach is used. Illustrative examples include safety assessment of an inelastic frame with uncertain properties. The study reported in chapter 4 considers a few inverse problems of structural safety analysis aimed at the determination of system parameters to ensure a target level of safety and (or) to minimize a cost function for problems involving combined probabilistic and non-probabilistic uncertainty modeling. Development of load and resistance factor design format, in problems with combined uncertainty models, is also presented. We employ super-ellipsoid based convex function/fuzzy variable models for representing non-probabilistic uncertainties. The target safety levels are taken to be specified in terms of indices defined in standard space of uncertain variables involving standard normal random variables and (or) unit hyper-spheres. A class of problems amenable for exact solutions is identified and a general procedure for dealing with more general problems involving nonlinear performance functions is developed. Illustrations include studies on inelastic frame with uncertain properties. A summary of contributions made in the thesis, along with a few suggestions for future research, are presented in chapter 5. Annexure A-F contain the details of derivation of alternative forms of safety measures, Newton Raphson’s based methods for optimization used in solutions to inverse problems, and details of combining Matlab based programs for uncertainty modeling with Abaqus based models for structural analysis.

Future design procedures for civil structures, especially those to be protected from extreme loads, will need to account for temporal evolution of their frequency content. Separate time analysis and frequency analysis by themselves do not fully describe the nature of these nonstationary dynamic loads. In the past few years, significant effort has been devoted to wavelets and time-frequency analysis. The appropriateness of emerging joint-time frequency analysis techniques for structural engineering problems is evaluated. Emphasis is focused on adaptive methods and the wavelet transform is also considered for validation purposes. In particular, the adaptive chirplet decomposition method and the empirical mode decomposition method are investigated. The required level of sophistication of the adaptive analysis is assessed. Mathematical expressions pertaining to time-frequency estimators are derived. Specifically, a transition from individual spectrograms to evolutionary power spectrum is attempted and function-specific decompositions are used for the estimation of the mean instantaneous frequency. Further, the Bootstrap method is employed for the assessment of the accuracy of the statistical estimators for the cases where limited data is available. An alternative approach utilizing function-specific decompositions for the derivation of well defined Hilbert spectra is suggested. Data pertaining to simulated and recorded earthquake signals, nonlinear structural responses due to earthquake excitations, and sea level recordings during the 2004 tsunami in Indian Ocean are used. The significance of the present study, over studies available in the literature for wavelets based structural analysis, hinges upon the consideration of adaptive and nonadaptive methods, the computational efficiency and effectiveness assessment of the suggested time-frequency estimators. It is expected that this study will enhance the interest in using advanced signal processing methods in structural systems analysis and design.

All real physical structures, when subjected to loads or displacements, behave dynamically. The additional inertia forces, from Newton’s second law, are equal to the mass times the acceleration.If the loads or displacements are applied very slowly then the inertia forces can be neglected and a static load analysis can be justified.Hence, dynamic analysis is a simple extension of static analysis. Many developments have been carried out in order to try to quantify the effects produced by dynamic loading. Examples of structures where it is particularly important to consider dynamic loading effects are the construction of tall buildings, long bridges under wind-loading conditions and buildings in earthquake zones, etc. Typical situations where it is necessary to consider more precisely the response produced by dynamic loading are vibrations due to equipment or machinery, impact load produced by traffic, snatch loading of cranes, impulsive load produced by blasts, earthquakes or explosions. So it is very important to study the dynamic nature of structures.

The present focuses on dynamic nature of various structures present in an environment where they are bound to undergo vibrations. In such vibrating conditions when they are subjected to a resonance they experience high amplitudes, leading to the failure of the structure. Hence, the study of operating frequencies of 1) Machine Foundations i) Los Angels Abrasion Machine ii) Jaw Crushing Machine 2) Fiber Reinforced Glass Composites – varying the number of layers i) 16 layers ii) 12 layers 3) Steel Flats In this study we have used a non computational technique for analysis of dynamic nature of structures. Brüel&Kjær PULSE™, Multi-analyzer System Type 3560 was used in the analysis. The operating frequency ranges in case of Los Angels Abrasion Machine is found to be 48 Hz – first frequency and 73 Hz – second frequency. In case of Jaw Crushing Machine is 42.2 Hz – first frequency and 71.8 Hz – second frequency. Where as, in case of steel flat the operating frequency is found to be 41.50 Hz. The fiber reinforced glass composites were decreased in area in a regular pattern and the pattern of frequency variation was observed. In case of 16 layers the first frequency decreased from 284 Hz – 236 Hz and the second frequency also depicted similar pattern. In case of 12 layers the first frequency decreased from 190 Hz – 160 Hz and the second frequency varied from 588 Hz – 390 Hz. The observed trend is justified as the value of K decreases as we decrease the area of the sample. We have also studied the determination of Buckling load from frequency study incase of a steel flat. When steel flat is subjected to increasing axial load the operating frequency is observed to decrease. When this operating frequency tends to zero the axial load nears the buckling load of that structure. 30cm steel flat is tested in a UTM under increasing axial load. The initial frequency under no load condition is 260 Hz. Under a load of 0.4 ton the first frequency decreases to 168 Hz. Extrapolating the decreasing trend we get the buckling load as 1.1739 ton. A similar trend was observed in case of second frequencies. The vibration analysis of the foundations of various machines will help us in designing them such that their serviceability is increased. Similarly, fiber reinforced composites are being used in various structural members. These demands require a deeper understanding of fiber composite behavior. Composites offer great promise as light weight and strong structural materials. The study of dynamic behavior of a structure holds atmost importance in evaluating its engineering performance and serviceability.

Optimization is the process of finding the best solution from a set of available solutions of a problem. The optimization problems in the field of mechanical engineering requires to maximize or minimize a mathematical function which represent a physical phenomenon. Traditional methods of solving optimization problems may provide exact solutions but largely fail to obtain good solution in reasonable computational time while solving complex nonlinear optimization problems because of trapping at local minima. Therefore, meta-heuristic techniques can be conveniently adopted to solve large-scale nonlinear problems for which it is difficult to obtain exact solutions by traditional methods. The capability of meta-heuristic approaches is not limited in solving particular type of problem; rather they can be applied to different types of optimization functions like linear, nonlinear, continuous, discrete etc. These algorithms do not guarantee exact solutions but produce solutions with required accuracy in finite time in most of the cases. Since engineers and practitioners need to design and manufacture products of superior quality at low cost in order to obtain competitive edge in the market place, optimization of product or process design and/ or operations of process is highly essential. The problems encountered in real world are mostly nonlinear in nature with restrictions in use of resources. Sometimes multiple conflicting objectives need to be satisfied. To solve such type of problems, meta-heuristic algorithms can be conveniently applied. Before applying the algorithms to solve real world problems, they must be tested with a variety of test problems. In this thesis, an efficient but simple meta-heuristic algorithm known as simple optimization algorithm (SOPT) is proposed to solve complex engineering problems. An improvement is made in the algorithm so that it should get escaped from the local optima whenever it gets stuck up. It is applied to solve twenty-five unconstrained benchmark functions of different characteristics. The results of optimization are compared with some of the well-known meta-heuristic techniques viz. artificial bee colony algorithm (ABC), particle swarm optimization (PSO), genetic algorithm (GA), shuffled frog leaping algorithm (SFLA), imperialistic competitive algorithm(ICA) and teaching learning based optimization(TLBO). Promising and comparable results are obtained for most of the test problems. Initial results encourage to further develop the SOPT algorithm for getting solution for constrained optimization problems. However, performance of an algorithm in solving constrained optimization problem depends on proper selection of constraint handling method. In this research, a constraint fitness priority based ranking method is used to handle constraints in SOPT algorithm. SOPT algorithm is applied to solve eighteen constrained problems. Some of these problems are continuous, some are restricted to take only integer values and some are of mixed type where some parameter take only integer values and others take any continuous value. These problems include eleven constrained single objective design and manufacturing optimization problems. Results of optimization from SOPT algorithm is compared with other meta-heuristic algorithms like GA, PSO, ABC, TLBO, differential evolution (DE), firefly algorithm (FA), league championship algorithm (LCA), water cycle algorithm (WCA) and mine blast algorithm (MBA) and some of the modified versions of these algorithms. To check stability of algorithm, it is run for thirty times to calculate mean result and standard deviation of results. Promising stable results are obtained in most of the problems. In engineering applications, often situation arises when optimization of multiple objectives, sometimes conflicting in nature, is required. In such cases, a closed form solution is difficult to obtain but a set of non-dominated solutions are generated to provide the decision maker a wide choice of selecting a solution depending on the situation. SOPT algorithm is incorporated with a dynamically weighted aggregation approach where multiple objectives are aggregated into a single objective through dynamically varying weights. To maintain uniformly distributed non-dominated solutions, a crowding distance approach is employed in SOPT algorithm. Multi-objective SOPT algorithm is applied to solve seventeen multi-objective problems from the literature including six engineering optimization problems. Sets of non-dominated solutions are obtained from multi-objective SOPT algorithm and these are compared with the results of non-dominated sorting based genetic algorithm II (NSGA II). To measure the quality of solutions, four metrics are defined - two metrics for finding closeness of obtained solutions from the best possible solutions and two are defined to check the diversity of solutions. Results indicate that SOPT algorithm delivers results comparable to NSGA II results. SOPT algorithm being a simple method to understand, easy to implement and able to solve variety of optimization problems including unconstrained and constrained, single and multi-objective problems, it becomes a good choice for solving real world engineering optimization problems

The main purpose of Structural Health Monitoring (SHM) is the assessment of structural conditions in aerospace, mechanical and civil systems. In structural engineering, damage is defined as any permanent change in the structural and geometric properties of a system caused by an external action. Vibration-based damage assessment methods rely on the use of sensors that record the structural dynamic response of a system that is determined by its structural and geometric properties. External disturbances and environmental conditions in which the system operates cause fluctuations of these properties and might hide the change in signature induced by damage. To handle the uncertainties in the determination of the structure’s characteristics, a statistical pattern recognition approach is presented in this thesis. Any statistical approach relies on the statistics of some features that provide a compact representation of the structural properties and that are sensitive to damage. Such features are called damage sensitive features and are extracted from the dynamic response of the structure: their statistical distribution is then analyzed to assess the occurrence of damage. This dissertation focuses on the analysis of the statistical distribution of damage sensitive features which are extracted through parametric and nonparametric algorithms. Cepstral coefficients are features defined in the field of acoustics and, in this thesis, they have been adapted to SHM analyses in order to develop compact damage sensitive features whose extraction requires a low computational effort. In this thesis, cepstral coefficients have been mathematically transformed through a Principal Component Analysis in order to generate damage sensitive features that are barely sensitive to measurement noise, environmental conditions and different excitation sources. In an attempt to develop an automated strategy for structural damage assessment, the search for damage sensitive features has been extended to the estimation of structural mode characteristics obtained through an output-only version of the Inner Product Vector methodology, e.g. considering only the structural response time histories. This new damage assessment procedure requires low computational effort and is capable to identify both the presence of damage and its location. However, one of the critical points of the proposed procedure consists in the manual evaluation of the spectral content of the dynamic responses that requires the user’s intervention. To automatize this procedure, a Bayesian clustering algorithm and a classifier have been successfully implemented and tested. Finally, the robustness of Bayesian regression algorithms to overfitting led us to consider their applicability to the field of system identification in order to provide a reliable estimate of the structural modal parameters that can be used as damage sensitive fea- tures. In fact, one of the main problems of system identification algorithms is that they rely on a regression algorithm that tends to overfit data producing unreliable results. Results provided by the Bayesian regression based system identification algorithm are obtained and compared with the ones coming from standard system identification algorithms.

Beams with variable cross-section and material properties are frequently used in aeronautical engineering, mechanical engineering and civil engineering (e.g., rotor shafts, beams, columns and functionally graded beams). Stepped beam-like structures are widely used in various engineering fields, such as robot arm and tall building, etc. Beams are a standout amongst the most usually utilized structural components within various structural elements in numerous engineering applications and experience a wide mixed bag of static and element loads. Fracture may create in beam like structures because of such loads. The progressions of cracks can severely decrease the stiffness of an element and further lead to the failure of the complete structure. Fractures or different blotch in a component of structural type impact its conduct dynamically and transform the coagulate and damping properties. Hence, the frequency occurred naturally and mode pattern of the structure hold data about the position and measurements of the defect. The presence of fracture in the structure are been subjected by the local flexibility which damages the behaviour dynamically of entire structure to a notable degree. Any investigation of these progressions makes it conceivable to inspect the fractures.