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Title:Reliability−based topology optimization frameworks for the design of structures subjected to random excitations
Author(s):Chun, Junho
Director of Research:Paulino, Glaucio H.
Doctoral Committee Chair(s):Paulino, Glaucio H.
Doctoral Committee Member(s):Song, Junho; Menezes, Ivan F.M.; Elbanna, Ahmed E.; Tovar, Andrés; Baker, William F.
Department / Program:Civil & Environmental Eng
Discipline:Civil Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Topology optimization
Stochastic excitation
Reliability-based design optimization
Reliability-based topology optimization
Parameter sensitivity
Discrete representation
Polygonal elements
Forced vibration optimization
System reliability
Sequential compounding method
First-passage probability
Ground structure
discrete filtering
Abstract:Structural optimization aims to provide structural designs that allow for the best performance while satisfying given design constraints. Among various applications of structural optimization, topology optimization based on mathematical programming and finite element analysis has recently gained great attention in research community as well as in applied structural engineering fields. One of the most fundamental requirements on building structures is to withstand various uncertain loads such as earthquake ground motions, wind loads and ocean waves. The design of structures, therefore, needs to ensure safe and reliable operations of structures over a prolonged period of time during which they may be exposed to various randomness of excitations caused by hazardous events. As such, significant amount of time and financial resources are invested to control the dynamic response of a structure under random vibrations caused by natural hazards or operations of non-structural components. In this regard, topology optimization of structures with stochastic response constraints is of great importance and consideration in industrial applications. This thesis discusses the development of structural optimization frameworks for a wide spectrum of deterministic and probabilistic constraints in engineering and investigate numerical applications. First, the efficient optimization framework for statics and dynamics problems is investigated. In many incidences, expensive computational cost and labor hours are so prohibitive that optimization processes become impractical or inapplicable. In order to alleviate the computational burden in dynamic topology optimization, the multiresolution topology optimization approach is adopted. Based on the polygonal finite element method and multiresolution topology optimization techniques, a method of polygonal multiresolution topology optimization for statics and dynamics problems is developed. This development provides methods to discretize complicated geometries and reduce computational cost to obtain topology results of high-resolutions. Despite rapid technological advances, incorporating stochastic response of structures into topology optimization is considered a relatively new field of research mainly due to computational challenges. In order to overcome such technical challenges in this field, a new method is introduced for incorporating random vibration theories into topology optimization using a discrete representation method for stochastic processes. Furthermore, a novel formulation is developed for sensitivity analysis of stochastic responses in order to use gradient-based optimization algorithms for the proposed topology optimization employing the discrete representation method. To assess the reliability of a structure subjected to random excitations, the probability of the occurrence of at least one failure event over a time interval, i.e. the first passage probability, often needs to be evaluated. In this thesis, a new method is proposed to incorporate probabilistic constraints on the first passage probability into structural design and topology optimization. To obtain the first passage probability effectively during each iteration, the failure event is described as a series system event consisting of failure events defined at discrete time points, and the system failure probability is obtained with the sequential compounding method. A new sensitivity formulation is developed employing the sequential compounding method to facilitate the use of gradient-based optimizers for the proposed method. Finally, the conventional filter effects are investigated in reliability-based topology optimization using the elastic formulation of the ground structure method. In addition, an optimization scheme employing the discrete filter is proposed to ensure that optimized solutions satisfy the probabilistic constraints and global equilibrium. In addition, the single-loop approach is incorporated to enhance the computational efficiency of the proposed RBTO method.
Issue Date:2016-07-15
Rights Information:© 2016 by Junho Chun. All rights reserved.
Date Available in IDEALS:2016-11-10
Date Deposited:2016-08

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