• An improved BESO method with adaptive evolutionary ratio (ER) significantly accelerates topology optimization for nonlinear structures, achieving up to 37.3% faster convergence compared to fixed ER.
• The method integrates Python with Abaqus for finite element analysis, enabling efficient handling of material and geometric nonlinearities.
• Four distinct adaptive ER functions are proposed and validated through benchmark cases, demonstrating consistent improvements in optimization efficiency.
• The approach extends the applicability of BESO to large-scale engineering structures and complex nonlinear problems, offering a robust tool for practical design.