Influence of mesh size, evolutionary rate, and filter radius on geometrically nonlinear topology optimization

Abstract

The BESO method is widely used to find efficient structural layouts through iterative material removal and addition. The method works well under linear conditions but things get more complicated when geometric nonlinearity is involved. Large displacements affect how the structure reaches equilibrium and this directly changes the sensitivity field and material update process making parameter selection much more critical. This paper studies three parameters systematically: mesh size, evolutionary rate and filter radius. Three benchmark structures are tested including an L-shaped beam, a pinned rectangular plate and a U-shaped plate. Each parameter is changed one at a time while the others stay fixed. Nodal displacement at the load point is used alongside topology results as a direct stiffness measure. Results show that the main load path stays intact across all tested cases but secondary bracing members are noticeably affected by coarser meshes, higher evolutionary rates and larger filter radii. The filter radius had the strongest overall influence on both topology and stiffness. The findings provide practical guidance for parameter selection and highlight the need to critically reassess algorithmic settings developed for linear BESO before applying them in large-displacement structural optimization.