Structural topology optimization based on an immersed FEM Level-Set method

In the present paper, we propose a parametrized Level Set (LS) approach based on a new Immersed Finite Element (FE)-LS strategy for Topology Optimization (ILSTO). Arbitrary design domains with generic boundaries are efficiently described by the proposed approach. Within this method, a generic FE discretization is mapped on a regular LS grid of knots, avoiding the TO problem from the necessity of postprocessing and filtering. In addition, using an approximating function for expressing the spatial derivatives and relying on a simple definition of reinitialization, the solution does not suffer from numerical instabilities, commonly associated with the calculation of the LS surface gradients. The proposed ILSTO method is benchmarked against conventional methods to demonstrate its improved geometrical resolution and numerical robustness, while maintaining computational efficiency.