A topology optimization method for managing transient thermal and vibration effects with eigenvalues and steady-state constraints

This paper presents a topology optimization method for the effective control of transient thermal conduction and vibration responses using eigenvalues and steady-state temperatures. Designing thermally efficient devices with transient responses, such as battery housings, is crucial for maximize operational efficiency. Eigenvalues were used to approximate the response, reducing the computational cost associated with the transient response in the optimization process. The objective functionals were evaluated using the weighted sum method. Maximum temperature constraints were incorporated into the eigenvalue problem by considering the steady-state temperature distribution. This study employed finite element analysis to solve the eigenvalue problems concerning vibration and heat transfer effects and to update the level-set functions. The effectiveness of this method was demonstrated by implementing two- and three-dimensional numerical examples, in which the thermal response was improved by maximizing the thermal eigenvalues, and the effects of thermoelasticity on the thermally efficient structures.