Thermo‐Mechanical Topology Optimization: An Immersed FEM Level‐Set‐Based Approach

This paper proposes a multi‐physics framework for topology optimization using an immersed level set‐finite element model. The work extends the capabilities of a recently developed immersed level‐set method to thermo‐mechanical problems, including coupling and material‐dependent properties. The objective functions are mechanical compliance and heat potential transport capacity. The sensitivity analysis allows capturing both nonlinearities in one velocity extension field. The level set evolution is parametrized using radial basis functions. Separate competing thermal and mechanical objective functions (regardless of their interconnection behavior) are considered using a linear combination. Numerical results confirm the method's effectiveness in handling conflicting performance goals, providing smooth topologies on domains with arbitrary shapes and boundary conditions. The results show that the proposed immersed level set method is an efficient and versatile tool for multi‐physics topology optimization, highlighting its potential for advanced engineering design applications.