Topology optimization for transient thermoelastic structures under time-dependent loads

Most of the previous topology optimization methods for thermoelastic structures use steady-state heat transfer and static equations, which are not applicable to time-dependent loads. In this article, a generic topology optimization method considering transient thermoelastic coupling is proposed based on transient heat transfer and dynamic equations. First, a thermoelastic coupling matrix is proposed to address the issues on calculation error of thermal stress loads and solution difficulty of adjoint multipliers under transient conditions. Second, a compact transient thermoelastic sensitivity equation with a distinct physical implication is derived based on adjoint sensitivity analysis. Finally, various comparative case studies of structural dynamics, transient heat conduction, and transient thermoelastic optimizations (including multi-material and 3D structures) are carried out to demonstrate the effectiveness, stability, and versatility of the proposed method. Additionally, this study discovers that the transient thermoelastic optimizations present strong transient effect, and the corresponding mechanism is also revealed. The proposed method can be widely used in structural optimization considering transient thermoelasticity under time-dependent loads.