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In many design problems, designers typically utilize finite element models to predict the behavior and assess the safety of a system. It is challenging to perform probabilistic analysis, and design a reliable system, because repeated finite element analyses of large models are required, and these models must be coupled with an optimizer, which is often prohibitively expensive. This thesis presents a methodology for probabilistic analysis and reliability based design optimization (RBDO) to overcome the above challenge. RBDO incorporates probabilistic reanalysis (PRRA) into the optimization process so that the optimum design has a great chance of staying in the feasible design space despite the inevitable variability in the design variables/parameters. PRRA calculates very efficiently the system reliability for many probability distributions of the design variables by performing a single Monte Carlo simulation. Another part of work integrates PRRA with two alternative methods to create a new design tool that can perform reliability based optimization efficiently. The first is Trust Region methodology and the second is a Global-Local methodology. These two methods are demonstrated and compared on a ten-bar truss structure.
This book provides readers with an understanding of the fundamentals and applications of structural reliability, stochastic finite element method, reliability analysis via stochastic expansion, and optimization under uncertainty. It examines the use of stochastic expansions, including polynomial chaos expansion and Karhunen-Loeve expansion for the reliability analysis of practical engineering problems.
This book – comprised of three separate volumes – presents the recent developments and research discoveries in structural and solid mechanics; it is dedicated to Professor Isaac Elishakoff. This third volume is devoted to non-deterministic mechanics. Modern Trends in Structural and Solid Mechanics 3 has broad scope, covering topics such: design optimization under uncertainty, interval field approaches, convex analysis, quantum inspired topology optimization and stochastic dynamics. The book is illustrated by many applications in the field of aerospace engineering, mechanical engineering, civil engineering, biomedical engineering and automotive engineering. This book is intended for graduate students and researchers in the field of theoretical and applied mechanics.
Uncertainties play a dominant role in the design and optimization of structures and infrastructures. In optimum design of structural systems due to variations of the material, manufacturing variations, variations of the external loads and modelling uncertainty, the parameters of a structure, a structural system and its environment are not given, fixed coefficients, but random variables with a certain probability distribution. The increasing necessity to solve complex problems in Structural Optimization, Structural Reliability and Probabilistic Mechanics, requires the development of new ideas, innovative methods and numerical tools for providing accurate numerical solutions in affordable computing times. This book presents the latest findings on structural optimization considering uncertainties. It contains selected contributions dealing with the use of probabilistic methods for the optimal design of different types of structures and various considerations of uncertainties. The first part is focused on reliability-based design optimization and the second part on robust design optimization. Comprising twenty-one, self-contained chapters by prominent authors in the field, it forms a complete collection of state-of-the-art theoretical advances and applications in the fields of structural optimization, structural reliability, and probabilistic computational mechanics. It is recommended to researchers, engineers, and students in civil, mechanical, naval and aerospace engineering and to professionals working on complicated costs-effective design problems.
Increasing demand on improving the resiliency of modern structures and infrastructure requires ever more critical and complex designs. Therefore, the need for accurate and efficient approaches to assess uncertainties in loads, geometry, material properties, manufacturing processes, and operational environments has increased significantly. Reliability-based techniques help develop more accurate initial guidance for robust design and help to identify the sources of significant uncertainty in structural systems. Reliability-Based Analysis and Design of Structures and Infrastructure presents an overview of the methods of classical reliability analysis and design most associated with structural reliability. It also introduces more modern methods and advancements, and emphasizes the most useful methods and techniques used in reliability and risk studies, while elaborating their practical applications and limitations rather than detailed derivations. Features: Provides a practical and comprehensive overview of reliability and risk analysis and design techniques. Introduces resilient and smart structures/infrastructure that will lead to more reliable and sustainable societies. Considers loss elimination, risk management and life-cycle asset management as related to infrastructure projects. Introduces probability theory, statistical methods, and reliability analysis methods. Reliability-Based Analysis and Design of Structures and Infrastructure is suitable for researchers and practicing engineers, as well as upper-level students taking related courses in structural reliability analysis and design.
Uncertainties play a dominant role in the design and optimization of structures and infrastructures. In optimum design of structural systems due to variations of the material, manufacturing variations, variations of the external loads and modelling uncertainty, the parameters of a structure, a structural system and its environment are not given, fi
Computational optimization plays an important role in engineering design, leading to greatly improved performance. Deterministic optimization, however, can result in undesired choices because it neglects uncertainty. Reliability-Based Design Optimization (RBDO) can provide optimum designs in the presence of uncertainties. The traditional double-loop RBDO approach based on First-Order Reliability Method (FORM) may be inaccurate, since it requires transformation from non-normal random variable space to standard normal variable space which, in certain circumstances, increases the nonlinearity of the limit state function(s). FORM may also be inefficient, because an iterative search process for the Most Probable Point (MPP) is required, resulting in a costly double-loop optimization algorithm. An RBDO with Mean Value First Order Saddlepoint Approximation (MVFOSA) algorithm is proposed with enhanced accuracy and almost the same efficiency with deterministic optimization. MVFOSA estimates the Probability Density Function (PDF) and the Cumulative Distribution Function (CDF) of the response using an accurate Saddlepoint approximation (SA). The limit state function is approximated using a first order Taylor series expansion at the mean values of the random input variables. MVFOSA is more accurate than FORM, because there is no transformation from non-normal to normal random variables and the iterative search process for the MPP is avoided. Examples demonstrate the proposed methodology. The extension to MVSOSA (Mean Value First Order Saddlepoint Approximation), based on a second order Taylor expansion is also proposed, in order to further increase the accuracy of the computed probability density functions, retaining the high efficiency by calculating the required Hessian matrix using quasi-second order saddlepoint approximation. Real life problems usually exhibit a multidimensional and multimodal behavior requiring a global optimization approach which is computationally inefficient. We propose a Design of Experiments (DOE) algorithm, which constructs optimal space filling designs in many dimensions with good projective properties. The algorithm also creates DOE groups with space filling properties and unions of these groups also retain space filling properties. The DOEs are obtained without optimization, improving computational efficiency. The proposed DOE algorithm can be used to create accurate metamodels (model(s) of an original model) sequentially and efficiently. Examples illustrate the concepts and demonstrate the applicability of the proposed method. We combine the DOE algorithm and MVSOSA methods into an integrated RBDO algorithm. The objective is to use MVFOSA and MVSOSA for black-box optimization problems by replacing the computation of first and second-order derivatives with a quadratic response surface, trained on design sites defined by the proposed DOE. The final step of this research was the development of a second-order Saddlepoint (SA) method for reliability analysis. The Advanced mean-Value Second-Order Saddlepoint Approximation (AMVSOSA) is proposed as an extension to the Mean-Value Second-Order Saddlepoint Approximation (MVSOSA). The proposed method is based on a second-order Taylor expansion of the limit state function around an approximate Most Probable Point (MPP) computed using a Mean-Value First-Order Second-Moment (MVFOSM) approach rather than the mean value of the random parameters as in MVSOSA.
Uncertainties about analytical models, fluctuations in loads, and variability of material properties contribute to the small but real probability of structure failures. This advanced engineering text describes methods developed to deal with stochastic aspects of structural behavior, providing a framework for evaluating, comparing, and combining stochastic effects. Starting with the general problem of consistent evaluation of the reliability of structures, the text proceeds to examination of the second-moment reliability index methods that describe failure in terms of one or more limit states. It presents first-order reliability methods for computation of failure probabilities for individual limit states and for systems; and it illustrates identification of the design parameters most affecting reliability. Additional subjects include a self-contained presentation of extreme-value theory and stochastic processes; stationary, evolutionary, and nonlinear aspects of stochastic response of structures; a stochastic approach to material fatigue damage and crack propagation; and stochastic models for several natural and manufactured loads.
In the current, increasingly aggressive business environment, crucial decisions about product design often involve significant uncertainty. Highlighting the competitive advantage available from using risk-based reliability design, Engineering Design Reliability Applications: For the Aerospace, Automotive, and Ship Industries provides an overview of