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.

中文翻译：

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使用 Tsai-Wu 准则对复合材料层合板进行应力控制的进化拓扑优化


在本研究中，提出了一种具有应力控制的复合材料层合板拓扑优化技术。选择双向进化结构优化 （BESO） 方法以避免应力奇异性。该技术根据 Tsai-Wu 准则表示失效指数，从而确保全面考虑各向异性。为了解决应力的局部性质和层压板的多层结构，采用了嵌套 p 范数，提供了局部最大失效指数的全局近似值。为了减轻高度非线性的应力行为，将过滤方案应用于灵敏度数字和设计变量。灵敏度数字是通过伴随灵敏度分析和拉格朗日乘数得出的，以解决基于应力和应力约束的问题。通过对各种示例和条件下的系统数值研究，对所提出的框架进行了验证，为复合材料层合板的拓扑行为提供了见解。这项研究强调了在复合材料中考虑不同的拉伸和压缩强度的重要性，这是一项关键创新。此外，还深入探讨了基于刚度、应力约束和基于应力的设计之间的关系。