Thermoelastic topology optimization of structural components at elevated temperatures considering transient heat conduction

This paper provides a compact and efficient 167-line MATLAB code for thermoelastic topology optimization considering transient heat conduction, in view of designing structural components subjected to thermo-mechanical loads. The thermo-mechanical response is determined through finite-element modeling and discretized in time with an implicit finite difference scheme. A density-based topology optimization procedure is developed and applied to a standard compliance minimization problem extended with thermal boundary conditions. The sensitivity analysis is carried out by means of the adjoint variable method in combination with the discretize-then-differentiate approach for computational efficiency. The proposed methodology and its implementation in MATLAB are explained in detail. Furthermore, numerical examples are presented to demonstrate the influence of several parameters with respect to the thermo-mechanical loading and the transient heat conduction analysis. The results show that the thermo-mechanical load ratio significantly affects the optimized topology, as well as the thermal response time related to the transient thermal loading. Finally, the effect of the time-dependent loading is investigated based on a weighted formulation for the objective function to influence the optimization and to obtain a more mechanically or thermally optimized structure.