Multi‐Material Structural Topology Optimization via Dynamic Body‐Fitted Multi‐Trimmed Mesh Evolution and Reaction–Diffusion‐Based Level‐Set Method

ABSTRACT This article presents a novel and efficient computational framework for multi‐material structural topology optimization (TO), integrating a dynamic body‐fitted multi‐trimmed (BMT) mesh evolution technique with a reaction–diffusion (RD)‐based level‐set (LS) formulation. The proposed method addresses major challenges in capturing complex structural boundaries and material‐phase interfaces with high geometric fidelity. Within this framework, multiple independent LS functions evolve under a system of RD equations, driven by smooth, projected topological sensitivity fields computed on a fixed background mesh of regular quadrilateral elements. To accurately represent the evolving multi‐material geometry, a high‐resolution BMT mesh is dynamically constructed at each iteration by multi‐trimming the background mesh along the zero‐isolines of the LS functions, using a combination of marching squares and marching triangles algorithms. The resulting BMT mesh enables sharp material delineation and improves numerical stability throughout the optimization process. Benchmark examples demonstrate the framework's ability to generate high‐quality topologies with smooth boundaries, reduced compliance, and robust convergence. The proposed method provides a promising tool for advancing multi‐material TO by combining precise interface tracking, flexible geometry representation, and enhanced computational efficiency.