A reaction diffusion-based level set method using body-fitted mesh for structural topology optimization

Abstract

The level set method can express smooth boundaries in structural topology optimization with the level set function’s zero-level contour. However, most applications still use rectangular/hexahedral mesh in finite element analysis, which results in zig-zag interfaces between the void and solid phases. We propose a reaction diffusion-based level set method using the adaptive triangular/tetrahedral mesh for structural topology optimization in this work. Besides genuinely expressing smooth boundaries, such a body-fitted mesh can increase finite element analysis accuracy. Unlike the traditional upwind algorithm, the proposed method breaks through the constraint of Courant–Friedrichs–Lewy stability condition with an updating scheme based on finite element analysis. Numerical examples for minimum mean compliance and maximum output displacement at specified positions, in both 2D and 3D, converge within dozens of iterations and present elegant structures.