V. Plevris, Doctoral Dissertation (PhD) "Innovative Computational Techniques for the Optimum Structural Design Considering Uncertainties", Institute of Structural Analysis and Seismic Research, School of Civil Engineering, National Technical University of Athens (NTUA), 2009.
Abstract
Uncertainties in structural mechanics, and in particular in the phase of analysis and design, can play an extremely important role, affecting not only the safety and reliability of structures and their mechanical components, but also the quality of their performance. The response of a structural system may be very sensitive to uncertainties in the material properties, manufacturing conditions, external loading and analytical or numerical modeling. In order to account for these issues, stochastic analysis methods have been developed over the last decades. The optimum result obtained by a deterministic optimization formulation that ignores scatter of any kind of the parameters affecting its response has limited value and reliability, as it can be severely affected by the uncertainties that are inherent in the model. The deterministic optimum can be associated with unaccepted probabilities of failure, or it can be vulnerable to slight variations of some uncertain parameters. The development of probabilistic analysis methods over the last two decades has stimulated the interest for considering also randomness and uncertainty in the formulation of structural design optimization problems. In order to account for uncertainties in a structural optimization framework, probabilistic-based formulations of the optimization problem have to be used, utilizing stochastic simulation and probabilistic analysis.
The goal of the thesis is to unify the concepts of probability-based safety analysis and structural optimization and provide the necessary numerical tools to deal with optimization problems considering uncertainties. This goal is addressed by developing algorithms for solving the probabilistic structural optimization problems encountered. In order to deal with these problems efficiently, various algorithms and methodologies have to be used, such as efficient single- and multi-objective optimizers and efficient stochastic problems formulations for the stochastic analysis process. Despite the advances on these issues, the computational cost for considering the uncertainties in a structural design optimization problem remains extremely large, especially for real-world large-scale problems with many design and/or random variables. To alleviate the computational burden, the implementation of Neural Network (NN) metamodels is also proposed in this thesis for further reducing the computational cost, providing acceptable numerical results at an affordable computational time.
The dissertation consists of nine chapters in total, plus the bibliography and three ap-pendices. It is organized as follows: following the introduction of Chapter 1, Chapter 2 deals with the concept of uncertainty in structural engineering in general. Chapter 3 presents the formulation of single objective optimization problems, while Chapter 4 discusses the multi-objective optimization problem. The basics of Neural Networks and their implementation in structural engineering are presented in Chapter 5. Chapter 6 discusses the problem of structural optimization considering uncertainties, where the basic problems of this kind, namely the Reliability-Based Design Optimization (RBDO), the Robust Design Optimization (RDO) and the combination Reliability-based Robust Design Optimization (RRDO) problems are presented, among others.
The numerical applications of the dissertation are divided into two parts, A and B, pre-sented in Chapters 7 and 8, respectively. Part A (Chapter 7) contains the deterministic optimization test examples, where uncertainties are not taken into account. In Part B (Chapter 8), the probabilistic optimization test examples are discussed, where uncertainties play a significant role.
Chapter 9 contains the conclusions, the original contribution of the thesis, and direc-tions for future research. Finally, the bibliography is presented followed by three appendices: Appendix A, containing the notation and symbols used in the dissertation; Appendix B with the acronyms and abbreviations used; and Appendix C with a listing of publications by the author.