RELIABILITY-BASED TOPOLOGY OPTIMIZATION OF CONTINUUM STRUCTURES CONSIDERING RANDOM FIELD LOAD UNCERTAINTY

This paper proposes an efficient reliability-based topology optimization (RBTO) method based on the polynomial chaos expansions (PCE) surrogate model to address design problems considering random field load uncer-tainty. To this end, a single-loop RBTO model is established to minimize the structural volume fraction under probabi-listic constraint defined by compliance response. The Karhunen-Loève (K-L) expansion is utilized to characterize the random field of loads, while Monte Carlo simulation is employed to estimate the probability of structural failure. In order to mitigate the substantial computational demands of Monte Carlo Simulation method in calculating structural response, the PCE is implemented as a surrogate model, effectively capturing the intricate nonlinear relationship between random field loads and structural compliance. A high-precision PCE surrogate model can be constructed using a limited number of high-fidelity finite element analysis samples, Once the explicit expression of the surrogate model is constructed, the failure probability can be directly calculated at random samples based on the surrogate model, without the need for further finite element analysis, thereby significantly reducing computational time without compromising accuracy. The sensitivity of the probabilistic constraint function with respect to design variables is thoroughly derived, and the optimization problem is addressed using the method of moving asymptotes (MMA). The efficacy and superiority of the proposed surrogate model-based RBTO method are validated through comparisons with an analytical model-based RBTO approach. In addition, the effects of failure probability thresholds, compliance limits, mean and standard deviations of load random fields, and correlation lengths on the optimization outcomes was discussed through four numerical examples. The results indicate that when uncertainty factors increase, the structure needs to consume more materials to resist the interference of uncertainty factors. In the bargain, the surrogate model-based RBTO method significantly reduces the computation time and improves the optimization efficiency compared to the analytical model-based RBTO approach.