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System Reliability-Based Design and Multiresolution Topology Optimization

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Title: System Reliability-Based Design and Multiresolution Topology Optimization
Author(s): Nguyen, Tam H.
Director of Research: Paulino, Glaucio H.; Song, Junho
Doctoral Committee Chair(s): Paulino, Glaucio H.
Doctoral Committee Member(s): Song, Junho; Hajjar, Jerome F.; Duarte, C. Armando; Penmetsa, Ravi C.; Sutradhar, Alok; Baker, William F.; Beghini, Alessandro
Department / Program: Civil & Environmental Eng
Discipline: Civil Engineering
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: Ph.D.
Genre: Dissertation
Subject(s): topology optimization design optimization multiresolution high resolution reliability finite element method multiresolution topology optimization (MTOP) reliability-based design optimization (RBDO) reliability-based topology optimization (RBTO) first-order reliability method (FORM) second-order reliability method (SORM) component reliability-based topology optimization (CRBTO) component reliability-based design optimization (CRBDO) system reliability-based topology optimization (SRBTO) system reliability-based design optimization (SRBDO) reliability index approach (RIA) performance measure approach (PMA) adaptive mesh refinement (AMR) matrix-based system reliability (MSR) reliability index approach performance measure approach component probability system probability single-loop double-loop first-order reliability method second-order reliability method density method projection density filter reliability-based design optimization reliability-based topology optimization reliability index optimal design topology risk computational cost uncertainty design variable density element displacement element adaptive adaptive mesh refinement efficient approach large-scale matrix-based
Abstract: Structural optimization methods have been developed and applied to a variety of engineering practices. This study aims to overcome technical challenges in applying design and topology optimization techniques to large-scale structural systems with uncertainties. The specific goals of this dissertation are: (1) to develop an efficient scheme for topology optimization; (2) to introduce an efficient and accurate system reliability-based design optimization (SRBDO) procedure; and (3) to investigate the reliability-based topology optimization (RBTO) problem. First, it is noted that the material distribution method often requires a large number of design variables, especially in three-dimensional applications, which makes topology optimization computationally expensive. A multiresolution topology optimization (MTOP) scheme is thus developed to obtain high-resolution optimal topologies with relatively low computational cost by introducing distinct resolution levels to displacement, density and design variable fields: the finite element analysis is performed on a relatively coarse mesh; the optimization is performed on a moderately fine mesh for design variables; and the density is defined on a relatively fine mesh for material distribution. Second, it is challenging to deal with system events in reliability-based design optimization (RBDO) due to the complexity of system reliability analysis. A new single-loop system RBDO approach is developed by using the matrix-based system reliability (MSR) method. The SRBDO/MSR approach utilizes matrix calculations to evaluate the system failure probability and its parameter sensitivities accurately and efficiently. The approach is applicable to general system events consisting of statistically dependent component events. Third, existing RBDO approaches employing first-order reliability method (FORM) can induce significant error for highly nonlinear problems. To enhance the accuracy of component and system RBDO approaches, algorithms based on the second-order reliability method (SORM), termed as SORM-based RBDO, are proposed. These technical advances enable us to perform RBTO of large-scale structures efficiently. The proposed algorithms and approaches are tested and demonstrated by various numerical examples. The efficient and accurate approaches developed for design and topology optimization can be applied to large-scale problems in engineering design practices.
Issue Date: 2011-01-14
Rights Information: Copyright 2010 Tam Hong Nguyen
Date Available in IDEALS: 2011-01-14
Date Deposited: December 2

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