Enhancing topology optimization with colored body-fitted mesh using adaptive filter, dual re-meshing strategy, and OOP programming paradigm

Abstract

This study introduces a novel topology optimization approach by employing power law-based material interpolation and adaptive filtering in the framework of the unstructured grids. As an extension of the established Solid Isotropic Material with Penalization (SIMP) method that utilizes the fixed structured mesh, the proposed Colored Body-Fitted Optimization (CBFO) method adopts the body-fitted grids to enhance efficiency, accuracy, and adaptability for diverse engineering applications. Notably, incorporating body-fitted meshes with intermediate density profiles enables improved flexibility in the numerical simulations and eliminates the need for re-meshing in each iteration. The dual re-meshing strategy drastically reduces computational costs, with only two re-meshing procedures required throughout the optimization process. This approach facilitates the generation of dense mesh regions around critical boundaries to augment solution accuracy while enabling sparse mesh configurations in the low-sensitivity regions, thereby boosting computational efficiency without compromising performance. The effectiveness, robustness, and efficiency of the CBFO method are validated through testing on multiple standard minimum compliance and compliant mechanism problems. The proposed optimization method can converge in dozens of iterations, obtain better objective function values, and save computational costs by up to 69 % compared to the previous method using the body-fitted mesh. Additionally, a concise MATLAB script implementing the proposed method using an Object-Oriented Programming (OOP) paradigm is provided in the appendix and the supplementary material, complete with annotations.