Structural topology optimization with strength and heat conduction constraints

• Topology optimization under stress and heat conduction constraints.
• Multi-physics problem involving linear elasticity and heat conduction.
• Thermal expansion effect included in the optimization.
• Optimal solution satisfying stress and heat conduction constraints.
• Different optima obtained for different thermal conditions.

In this research, a topology optimization with constraints of structural strength and thermal conductivity is proposed. The coupled static linear elastic and heat conduction equations of state are considered. The optimization problem was formulated; viz., minimizing the volume under the constraints of p-norm stress and thermal compliance introducing the qp-relaxation method to avoid the singularity of stress-constraint topology optimization. The proposed optimization methodology is implemented employing the commonly used solid isotropic material with penalization (SIMP) method of topology optimization. The density function is updated using sequential linear programming (SLP) in the early stage of optimization. In the latter stage of optimization, the phase field method is employed to update the density function and obtain clear optimal shapes without intermediate densities. Numerical examples are provided to illustrate the validity and utility of the proposed methodology. Through these numerical studies, the dependency of the optima to the target temperature range due to the thermal expansion is confirmed. The issue of stress concentration due to the thermal expansion problem in the use of the structure in a wide temperature range is also clarified, and resolved by introducing a multi-stress constraint corresponding to several thermal conditions.