Transient heat conduction in multi-material topology optimization of thermoelastic structures involving dynamic constraints

This work presents a modified solid isotropic material with penalization (SIMP) for conducting dynamic-constrained multi-material topology optimization (MMTO) of thermoelastic structures subjected to transient thermal conduction. The novelty of this study is the multi-material optimization of instantaneous temperature conduction under specific frequency constraints, which has never been studied before. The proposed method has been developed for general models of multi-material interpolations such as thermal stiffness, heat capacity, and thermal stress coefficient. The temperature environment is formulated by applying prescribed mechanical and thermal loads that are exposed over a period of time. In this work, we focus on the objective of minimizing compliance in a transient heat conduction structure while simultaneously imposing constraints on the dynamics. With high temperatures, the stiffness of the optimization results decreases while stability is still guaranteed. The sensitivity of the objective function is subsequently calculated using the discretize-then-differentiate approach for the dynamic problem as well as the adjoint variable method. This study examines the impact of thermal fields and different time increments in conjunction with dynamic criteria. The outcomes of heat conduction result in notable alterations under identical dynamic constraint levels.