A multi-resolution method for 3D multi-material topology optimization

This paper presents a multi-resolution implementation in 3D for multi-material topology optimization problem. An alternating active-phase algorithm where the problem at hand is divided into a series of the traditional material–void phase topology optimization is employed for the multi-material problem. Different levels of discretization are used for the displacement mesh, design variable mesh and density mesh which provides higher resolution designs for the solutions. A projection scheme is employed to compute the element densities from design variables and control the length scale of the material density. Simple block coordinate descent method similar to the Gauss–Seidel technique is used to solve the subproblems. Several 3D numerical examples are presented to demonstrate the ease and the effectiveness of the proposed implementation. Incorporating the multi-resolution method into the multi-material approach, robust designs with improved resolution can be achieved for real life problems with complex geometries.