Stress-based Bi-directional Evolutionary Structural Optimization Method with Incremental Nonlinear Structural Analysis

Abstract

To extend the applicability of optimization methods in civil engineering, particularly for structural members incorporating cement-based materials like concrete, this study proposes a stress-based bi-directional evolutionary structural optimization (BESO) framework integrated with incremental nonlinear structural analysis. The core objective is to minimize peak stress in structures by leveraging the p-norm function (p = 4–6) to approximate stress concentration and sensitivity numbers derived via the adjoint method. The proposed approach is validated for optimizing structures with highly nonlinear material behaviors. By tuning the p-value (4–6) during optimization, solutions aligned with predetermined objectives are achieved through element sensitivity analysis. The sensitivity numbers are computed by filtering initial values derived from incremental nonlinear stress analysis results. Subsequent sensitivity filtering and iterative design variable updates ensure convergence to stable solutions matching the optimization goals. The method incorporates von Mises stress for nonlinear material modeling and addresses numerical challenges like mesh dependency through dual filtering strategies as verified by two-dimensional/three-dimensional examples including irregular beams and cantilever structures. This framework provides a robust tool for topology optimization of civil structures with strongly nonlinear materials, balancing accuracy and computational efficiency under volume constraints.