Robust topology optimization for structures under thermo-mechanical loadings considering hybrid uncertainties

As the growing demand of the performances for modern equipment under complex service condition, more challenges have been presented for topology optimization design considering the influence of thermo-mechanical coupling field. At present, most thermo-mechanical topology optimizations are focused on deterministic assumptions. However, the random and interval hybrid uncertainties related to material properties, loadings, etc. unavoidably exist in structures and may have notable influence on structural performances or even result in failure designs. This paper will develop a new robust topology optimization method for structures under thermo-mechanical loadings considering hybrid uncertainties, in which an efficient dimension reduction-based orthogonal polynomial expansion method is developed for hybrid uncertainty analysis. Firstly, the robust objective function is defined by the lower order moments and the topology optimization model is provided under the worst case. Based on the proposed hybrid uncertainty analysis method, the sensitivities with respect to the design variables are obtained. Finally, the gradient-based optimization method is applied to achieve the robust design for structures with thermo-mechanical loadings.