Assessing Finite Element Choice in Structural Topology Optimization and A Posteriori Error Estimation
For researchers in structural optimization, this work provides a comparative assessment of element choices, but the findings are incremental and confirm known trade-offs.
This study compares linear (P1) and quadratic (P2) triangular elements with bi-linear quadrilateral (Q1) elements in structural topology optimization using SIMP, finding notable differences in compliance and solution accuracy across benchmark problems.
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.