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    Robust and Reliability-Based Structural Topology Optimization Using a Continuous Adjoint Method

    Source: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering:;2016:;Volume ( 002 ):;issue: 003
    Author:
    Dimitrios I. Papadimitriou
    ,
    Costas Papadimitriou
    DOI: 10.1061/AJRUA6.0000869
    Publisher: American Society of Civil Engineers
    Abstract: A unified framework for robust and reliability-based structural topology optimization, considering structural model and loading uncertainties, is presented using a continuous adjoint formulation. The topology optimization is formulated for objective functions related to uncertainty measures of the compliance or displacements of the structure. Uncertainty measures, such as mean, standard deviation, and level exceedance probability or failure probability, involve the estimation of multidimensional integrals over the uncertain parameter space. These integrals are evaluated using (1) sparse grid quadrature techniques for the mean and standard deviation and (2) the approximate first-order reliability method (FORM) for failure probability. A unified continuous adjoint formulation is presented for the different objective function formulations. Simplifications are proposed that result in increased computational efficiency and accuracy for special cases of uncertainties and structural performance measures. The proposed formulation is demonstrated by computing the optimal distribution of material in a two-dimensional structure under loading and material uncertainties. For the approximate FORM-based topology optimization, computational difficulties are pointed out because of the existence of multiple design points in the uncertain parameter space.
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      Robust and Reliability-Based Structural Topology Optimization Using a Continuous Adjoint Method

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    http://yetl.yabesh.ir/yetl1/handle/yetl/83329
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    • ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering

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    contributor authorDimitrios I. Papadimitriou
    contributor authorCostas Papadimitriou
    date accessioned2017-05-08T22:35:59Z
    date available2017-05-08T22:35:59Z
    date copyrightSeptember 2016
    date issued2016
    identifier other51322964.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/83329
    description abstractA unified framework for robust and reliability-based structural topology optimization, considering structural model and loading uncertainties, is presented using a continuous adjoint formulation. The topology optimization is formulated for objective functions related to uncertainty measures of the compliance or displacements of the structure. Uncertainty measures, such as mean, standard deviation, and level exceedance probability or failure probability, involve the estimation of multidimensional integrals over the uncertain parameter space. These integrals are evaluated using (1) sparse grid quadrature techniques for the mean and standard deviation and (2) the approximate first-order reliability method (FORM) for failure probability. A unified continuous adjoint formulation is presented for the different objective function formulations. Simplifications are proposed that result in increased computational efficiency and accuracy for special cases of uncertainties and structural performance measures. The proposed formulation is demonstrated by computing the optimal distribution of material in a two-dimensional structure under loading and material uncertainties. For the approximate FORM-based topology optimization, computational difficulties are pointed out because of the existence of multiple design points in the uncertain parameter space.
    publisherAmerican Society of Civil Engineers
    titleRobust and Reliability-Based Structural Topology Optimization Using a Continuous Adjoint Method
    typeJournal Paper
    journal volume2
    journal issue3
    journal titleASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
    identifier doi10.1061/AJRUA6.0000869
    treeASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering:;2016:;Volume ( 002 ):;issue: 003
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
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