A body-fitted adaptive mesh and Helmholtz-type filter based parameterized level-set method for structural topology optimization

Parameterized level-set method (PLSM) has been proposed and developed for many years, and is renowned for its efficacy in addressing topology optimization challenges associated with intricate boundaries and nucleation of new holes. However, most pertinent investigations in the field rely predominantly on fixed background mesh, which is never remeshed. Consequently, the mesh element partitioned by material interface during the optimization process necessitates approximation by using artificial interpolation models to obtain its element stiffness or other properties. This paper introduces a novel approach to topology optimization by integrating the PLSM with body-fitted adaptive mesh and Helmholtz-type filter. Primarily, combining the PLSM with body-fitted adaptive mesh enables the regeneration of mesh based on the zero level-set interface. This not only precludes the direct traversal of the material interface through the mesh element during the topology optimization process, but also improves the accuracy of calculation. Additionally, the incorporation of a Helmholtz-type partial differential equation filter, relying solely on mesh information essential for finite element discretization, serves to regulate the topological complexity and the minimum feature size of the optimized structure. Leveraging these advantages, the topology optimization program demonstrates its versatility by successfully addressing various design problems, encompassing the minimum mean compliance problem and minimum energy dissipation problem. Ultimately, the result of numerical example indicates that the optimized structure exhibits a distinct and smooth boundary, affirming the effective control over both topological complexity and the minimum feature size of the optimized structure.