Evolutionary Topology Optimization with Stress Control for Composite Laminates Using Tsai-Wu Criterion

Abstract

To consider the multi-layer structure and distinct tensile and compressive strength, a topology optimization technique with stress control is proposed based on the bi-directional evolutionary structural optimization (BESO) method for the composite laminates. The approach adopts a linear material interpolation scheme and expresses the failure index based on the Tsai-Wu criterion. To address the multi-layer structure of laminates, a nested p-norm is employed to globally approximate the local maximum failure index. Sensitivity numbers are determined by adjoint sensitivity analysis and Lagrange multipliers for stress-based and stress-constrained designs. Filter schemes for both sensitivity numbers and design variables are applied to improve stability. Numerical investigations are conducted to validate the proposed technique. The importance of considering diverse tensile and compressive strengths in composite materials is demonstrated. Relations of stiffness-based, stress-constrained, and stress-based designs are explored.

Keywords: Topology optimization, BESO method, Composite laminate, Tsai-Wu criterion, Stress control