Bi-Directional Evolutionary Topology Optimization with Adaptive Evolutionary Ratio for Nonlinear Structures

Abstract

Current topology optimization methods for nonlinear continuum structures often suffer from low computational efficiency and limited applicability to complex nonlinear problems. To address these issues, this paper proposes an improved bi-directional evolutionary structural optimization (BESO) method tailored for maximizing stiffness in nonlinear structures. The optimization program is developed in Python and can be combined with Abaqus software to facilitate finite element analysis (FEA). To accelerate the speed of optimization, a novel adaptive evolutionary ratio (ER) strategy based on the BESO method is introduced, with four distinct adaptive ER functions proposed. The Newton-Raphson method is utilized for iteratively solving nonlinear equilibrium equations, and the sensitivity information for updating design variables is derived using the adjoint method. Additionally, this study extends topology optimization to account for both material nonlinearity and geometric nonlinearity, analyzing the effects of various nonlinearities. A series of comparative studies are conducted using benchmark cases to validate the effectiveness of the proposed method. The results show that the BESO method with adaptive ER significantly improves the optimization efficiency. Compared to the BESO method with a fixed ER, the convergence speed of the four adaptive ER BESO methods is increased by 37.3%, 26.7%, 12% and 18.7%, respectively. Given that Abaqus is a powerful FEA platform, this method has the potential to be extended to large-scale engineering structures and to address more complex optimization problems. This research proposes an improved BESO method with novel adaptive ER, which significantly accelerates the optimization process and enables its application to topology optimization of nonlinear structures.