热应力载荷条件下结构拓扑优化设计

Structural topology optimization of thermo-elastic problems is investigated in this paper. The key issues related to the penalty models of the element stiffness and thermal stress load of the finite element model are highlighted. To characterize the dependence of the thermal stress load upon the design variables defined by element densities, we apply the penalization to the thermal stress coefficient measured by the product between thermal expansion coefficient and Young’s modulus for the first time. In such a way, the element stiffness and the thermal stress load can be simultaneously penalized in terms of element pseudo-density. Besides, the RAMP is adopted as the interpolation model after a full study and comparison with the SIMP. Furthermore, sensitivity analysis of the structural mean compliance is developed in the case of steady-state heat conduction. This formulation demonstrates especially its capability of solving problems with multiphase materials. Numerical examples of two-phase and three-phase materials are dealt with.