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Reliability-Based Topology Optimization of Thermo-Elastic Structures with Stress Constraint

Author

Listed:
  • Liang Zhang

    (School of Mechanical and Electrical Engineering, Qingdao University, Qingdao 266071, China)

  • Qinghai Zhao

    (School of Mechanical and Electrical Engineering, Qingdao University, Qingdao 266071, China
    National Engineering Research Center for Intelligent Electrical Vehicle Power System, Qingdao University, Qingdao 266071, China)

  • Jianliang Chen

    (School of Mechanical and Electrical Engineering, Qingdao University, Qingdao 266071, China)

Abstract

Traditional topology optimization of thermo-elastic structures is based on deterministic conditions, without considering the influence of uncertainty factors. To address the impact uncertainty on structural strength, a reliability-based topology optimization of thermo-elastic structure with stress constraint is proposed. The probabilistic uncertainty quantities are associated with the structural material property, mechanical loads and the thermal stress coefficient with the topology optimization formulation considering volume minimization and stress constraint. The relaxation stress method combined with normalized p-norm function is adopted to condense whole element stresses into the global stress measurement that approximates the maximum stress. The adjoint variable method is utilized to derive the sensitivity of the stress constraint and the optimization problem is solved by the method of moving asymptote (MMA). Finally, several numerical examples are presented to demonstrate the effectiveness and validity of the proposed approach. Compared with the deterministic design, the reliability design has distinct topological configurations and the optimized structures maintain a higher reliability level.

Suggested Citation

  • Liang Zhang & Qinghai Zhao & Jianliang Chen, 2022. "Reliability-Based Topology Optimization of Thermo-Elastic Structures with Stress Constraint," Mathematics, MDPI, vol. 10(7), pages 1-22, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1091-:d:781369
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    References listed on IDEAS

    as
    1. Xiao, Mi & Zhang, Jinhao & Gao, Liang, 2020. "A system active learning Kriging method for system reliability-based design optimization with a multiple response model," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    2. Xiao Wang & Juan Wang & Xin Wang & Chujun Yu, 2022. "A Pseudo-Spectral Fourier Collocation Method for Inhomogeneous Elliptical Inclusions with Partial Differential Equations," Mathematics, MDPI, vol. 10(3), pages 1-18, January.
    3. Wang, Fajie & Zhao, Qinghai & Chen, Zengtao & Fan, Chia-Ming, 2021. "Localized Chebyshev collocation method for solving elliptic partial differential equations in arbitrary 2D domains," Applied Mathematics and Computation, Elsevier, vol. 397(C).
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