Topology optimization of thermo‐elastic structures considering stiffness, strength, and temperature constraints over a wide range of temperatures

Abstract

AbstractThis article proposes a thermo‐elastic topology optimization with stiffness, strength, and temperature constraints involving a wide range of temperatures. The state equations for the linear elasticity and heat conduction are considered. Formulations involving minimum volume with compliance, stress and temperature limits under multiple thermal conditions are presented. The global stress and regional temperature metrics adopting the corrected aggregation function are used to evaluate the maximal stress and temperature, respectively. The stress stabilizing scheme is utilized to overcome the iteration oscillation stemming from highly nonlinear behavior of thermal stress constraints for multiple thermal conditions. To achieve clear optimized topologies under design‐dependent loads, a continuation strategy for the relaxed Heaviside function is developed. Two 2D numerical examples are employed to illustrate the validity and practicability of the proposed approach. The results show that the optimized structures designed by a certain temperature may be damaged or have thermal deformations once the ambient temperature changes due to the thermal residual stress. The designs covering wide temperature range achieved by neglecting stiffness or strength constraints can result in stiffness reduction or strength failure. It is therefore imperative for the optimization to adopt a multi‐physics model involving multi‐constraints over a wide temperature range.