Level set topology optimization of structures under stress and temperature constraints

In this paper, we introduce a level set topology optimization formulation considering coupled mechanical and thermal loads. Examples considering stress and compliance minimization under temperature and volume constraints, and mass minimization under stress and temperature constraints, are presented. The p-norm of the stress field and temperature field is used to approximate the maximum stress and temperature, respectively. We show that the minimal compliant topologies under temperature constraints do not necessarily have low stress values, and the stress and temperature requirements can be conflicting. The results also show that designs obtained by ignoring the thermal or structural constraints can result in high values of temperature or stress, respectively, thus demonstrating the importance of using a coupled multi-physics model in the optimization