Stress-based evolutionary topology optimization via XIGA with explicit geometric boundaries

Abstract

This paper presents a novel approach to stress-based topology optimization that employs NURBS representations of explicit geometric boundaries to address stress minimization and stress-constrained problems. The proposed methodology is compatible with CAD systems and utilizes Extended IsoGeometric Analysis (XIGA) to ensure an accurate representation of stress field in the evolving structure. A p-norm aggregation scheme is used to measure global stress levels, and the aggregated stress constraint is augmented to the objective (compliance) via a Lagrange multiplier in stress-constrained problems. The proposed approach introduces a novel and efficient Lagrange multiplier trail strategy aimed at reducing computational costs. Additionally, a normalization scheme and a partial differential equation filter are presented to stabilize the highly nonlinear stress-based optimization. Validation studies demonstrate the effectiveness and characteristics of the proposed approach. Moreover, control points of the structural design can be directly edited to further improve strength performance. Comparative studies show clear advantages of the proposed methodology in terms of computational efficiency compared to other Finite element analysis (FEA)-based optimization methods. Overall, this paper presents a practical and novel approach that addresses the limitations of existing FEA-based optimization methods in terms of accuracy, flexibility, and degree of freedom (DOF) cost, and makes a significant contribution to the field of stress-based topology optimization.