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Date of Publication:2022-10-06

Journal:固体力学学报

Volume:39

Issue:1

Page Number:69-79

ISSN No.:0254-7805

Abstract:Topology optimization aims to find the optimal distribution of a given
   amount of material in a design domain to maximize the structural
   performance.However,the deterministic topology optimization may generate
   a structural design that is not reliable or robust under uncertain
   parameter variations.The reliability-based topology optimization
   considering spatially varying uncertain material properties is developed
   in this paper.In practical engineering,some uncertain parameters
   fluctuate not only over the time domain but also in space.Therefore,an
   independent random variable is incapable of characterizing the
   structural uncertainty due to its spatially varying nature.In such
   circumstances,we introduce a random field model for the spatially
   varying physical quantities.The elastic modulus is modeled as a random
   field with a given probability distribution,which is discretized by
   means of an Expansion Optimal Linear Estimation (EOLE).The response
   statistics and their sensitivities are evaluated with the polynomial
   chaos expansions (PCE).The accuracy of the proposed method is verified
   by the Monte Carlo simulations.The reliability of the structure is
   analyzed using the first-order reliability method(FORM).Two approaches
   to solving the optimization problems are compared,which are the
   double-loop approach and the sequential approximate
   programming(SAP)approach.Numerical examples show that the proposed
   method is valid and efficient for both 2Dand 3Dtopology optimization
   problems.The obtained results show that the SAP approach has higher
   efficiency than the double-loop approach,and can realize concurrent
   convergence of topology optimization and reliability analysis.In
   addition,it is found that the reliability-based topology
   optimization(RBTO) solutions considering the uncertain model(the random
   variable and the random field model)have different topologies and member
   sizes to improve the level of reliability as compared with the
   deterministic solutions. Also,the optimal designs considering the random
   field model require less material,compared with those obtained with
   random variables.

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