<p>To ensure that compliant mechanisms meet fatigue reliability requirements, a fatigue reliability-based topology optimization framework of compliant mechanisms considering material uncertainties is proposed in this paper. Considering the spatial distribution uncertainty of the material, the method employs random field to describe the elastic modulus. Polynomial chaos expansion is used to approximate the stochastic response of mechanism. The modified Goodman fatigue criterion is employed to establish fatigue constraints, and these constraints are aggregated by a Kieisselmeier–Steinhauser function. The objective function aims to minimize the volume of the mechanism under an output displacement constraint and a fatigue failure constraint. The proposed framework for fatigue reliability-based topology optimization of compliant mechanisms is organized as a nested double loop, where the outer loop is solved via the method of moving asymptotes to carry out topology optimization and the inner loop employs the hybrid mean value method for reliability analysis to find the minimum performance target point. Numerical examples validate the effectiveness of the proposed method. Compared with the deterministic topology optimization results, the compliant mechanisms obtained via the proposed method exhibit better fatigue reliability. Monte Carlo simulations are employed to validate the accuracy of the proposed method.</p>

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Fatigue reliability-based topology optimization of compliant mechanisms considering material uncertainties

  • Jinqing Zhan,
  • Xueqing Zhu,
  • Benliang Zhu,
  • Min Liu

摘要

To ensure that compliant mechanisms meet fatigue reliability requirements, a fatigue reliability-based topology optimization framework of compliant mechanisms considering material uncertainties is proposed in this paper. Considering the spatial distribution uncertainty of the material, the method employs random field to describe the elastic modulus. Polynomial chaos expansion is used to approximate the stochastic response of mechanism. The modified Goodman fatigue criterion is employed to establish fatigue constraints, and these constraints are aggregated by a Kieisselmeier–Steinhauser function. The objective function aims to minimize the volume of the mechanism under an output displacement constraint and a fatigue failure constraint. The proposed framework for fatigue reliability-based topology optimization of compliant mechanisms is organized as a nested double loop, where the outer loop is solved via the method of moving asymptotes to carry out topology optimization and the inner loop employs the hybrid mean value method for reliability analysis to find the minimum performance target point. Numerical examples validate the effectiveness of the proposed method. Compared with the deterministic topology optimization results, the compliant mechanisms obtained via the proposed method exhibit better fatigue reliability. Monte Carlo simulations are employed to validate the accuracy of the proposed method.