Assessing Finite Element Choice in Structural Topology Optimization and A Posteriori Error Estimation

TL;DR

This paper examines how the choice of finite elements affects the accuracy and outcomes of structural topology optimization using the SIMP method, emphasizing the importance of element type on solution quality.

Contribution

It provides a comparative analysis of linear, quadratic, and bi-linear finite elements in topology optimization and evaluates their impact using an a posteriori error estimator.

Findings

Quadratic elements improve solution accuracy over linear elements.

Finite element choice significantly influences the optimized structure's compliance.

A posteriori error estimation helps assess solution quality across different element types.

Abstract

This study investigates the impact of finite element selection on structural topology optimization using the SIMP (Solid Isotropic Material with Penalization) method. Specifically, it compares linear (P1) and quadratic (P2) triangular elements with the conventional bi-linear quadrilateral (Q1) elements. Numerical experiments performed on benchmark problems including a cantilever beam, a bridge structure, and a beveled beam reveal notable differences in both the final optimized objective value (compliance) and the accuracy of the finite element solutions. The accuracy is evaluated using an a posteriori error estimator, highlighting the influence of element type on solution quality and optimization performance.