Efficient phase field structural design algorithm for reliability-based topology optimization with material uncertainties

초록

Reliability-based topology optimization is the approach that incorporates uncertainty quantification into topology optimization to achieve robustness and reliability. In this paper, we propose a reliability-based topology optimization algorithm that integrates a phase-field model with uncertainty quantification techniques. Material uncertainty in Young's modulus is modeled as a random field and reduced via the Karhunen-Lo & egrave;ve expansion. A sequential optimization and reliability assessment strategy is adopted to decouple the optimization and reliability evaluation for reducing computational complexity. The topology optimization problem is solved by using the coupled finite element and finite difference approach, in which time integration is performed using a second-order Crank-Nicolson scheme. Reliability analysis is conducted by using the inverse reliability analysis method, with the limit-state function approximated by a stochastic response surface method. Monte Carlo simulations are performed to validate the accuracy of the computed failure probabilities. Numerical results confirm the efficiency and robustness of the proposed method in generating reliable structures under material uncertainty.

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