Evolutionary topology optimization with stress control for composite laminates using Tsai-Wu criterion

Abstract

In this study, a topology optimization technique with stress control is proposed for the composite laminates. The bi-directional evolutionary structural optimization (BESO) method is selected to avoid the stress singularity. The technique expresses the failure index based on the Tsai-Wu criterion, thereby ensuring a comprehensive consideration of the anisotropy. To address the local nature of stress and multi-layer structure of laminates, a nested p-norm is employed, providing a global approximation of the local maximum failure index. To mitigate the highly non-linear stress behaviors, filter schemes are applied to both sensitivity numbers and design variables. Sensitivity numbers are derived via adjoint sensitivity analysis and Lagrange multipliers to address stress-based and stress-constrained problems. The proposed framework is validated through systematic numerical studies across various examples and conditions, offering insights into the topological behaviors of composite laminates. This study underscores the importance of considering distinct tensile and compressive strength in composite materials, which represents a key innovation. Additionally, the relationships among stiffness-based, stress-constrained, and stress-based designs are explored in depth.