Regularization of topology optimization problem by the FEM a posteriori error estimator

TL;DR

This paper introduces a novel regularization technique for topology optimization that employs a posteriori finite element error estimators to improve solution quality and prevent checkerboard patterns.

Contribution

The authors propose a new regularization method based on FEM a posteriori error estimators to enhance topology optimization results and suppress checkerboard artifacts.

Findings

Reduces checkerboard patterns in optimized topologies

Provides higher regularity of solutions

Increases robustness of the optimization results

Abstract

In our work, we consider the classical density-based approach to topology optimization. We propose the modification of the discretized cost/objective functional using a posteriori error estimator for the finite element method. It can be regarded as a new technique to prevent checkerboards. It also provides higher regularity of the solutions and robustness of the results.