Lightweight topology optimization of thermal structures under compliance, stress and temperature constraints

This paper proposes a topology optimization method for a multi-physics problem considering weight minimization with compliance, stress, and temperature constraints. Two static equations for thermal and structural problems are solved. A novel topology optimization formulation, i.e., lightweight design involving compliance, stress and temperature limits, is established using the rational approximation of material properties. A corrected P-norm function is employed to exactly evaluate the maximum stress and temperature of the structure. Moreover, iteration oscillations stemming from the high non-linearity of stress constraint are alleviated by means of a stabilizing control scheme based on the stability transformation method. The sensitivity analysis of the coupled multi-physics field is performed utilizing the adjoint method. Some numerical examples are adopted to demonstrate the validity and robustness of the proposed methodology. It is indicated that the topology considering the above three constraints simultaneously can achieve good mechanical and thermal performances, while the compliance constraint can accelerate the rate of convergence. The stricter compliance limit leads to a heavier structure and more uneven stress distribution but less iterations. The optimized topologies are dependent on the temperature range due to the effect of thermal expansion.