This paper introduces a novel computational design framework for topology and fiber path optimization of variable stiffness laminated composites. Based on the finite element discretization of the design domain, the topology and material stiffness are represented using elemental densities and lamination parameters (LPs), respectively. The density distribution is optimized via the discrete-variable topology optimization to obtain a precise structural layout. The recently proposed Topological Derivative-based Sensitivity Analysis is extended to calculate discrete-variable sensitivities for anisotropic materials, where the formulation accuracy is verified by finite difference computations. Elemental stiffness properties are described through the LPs, which are used with discrete-variable topology optimization for the first time. Specifically, the lamination parameter interpolation method (LPIM) is employed to significantly reduce the number of design variables while ensuring smooth variation of fiber angles throughout the laminate. In addition, unlike the previous LPIM-based works involving only master points for LP interpolation, the concept of master lines is introduced to enlarge the design space for stiffness distribution. Elemental densities and LPs are iteratively optimized to avoid solving the mixed integer programming problem directly. The effectiveness of the developed methodology is demonstrated through various case studies where designs providing minimum compliance or maximum directed displacement at specific locations are determined. The results show that the proposed approach can efficiently provide optimal variable stiffness laminate designs with clear density distributions and manufacturable fiber paths.

中文翻译：

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将离散变量各向异性拓扑优化与基于层合参数插值的刚度定制集成

本文介绍了一种新的计算设计框架，用于可变刚度层压复合材料的拓扑和纤维路径优化。基于设计域的有限元离散化，拓扑和材料刚度分别使用单元密度和层合参数 （LP） 表示。通过离散变量拓扑优化优化密度分布，以获得精确的结构布局。最近提出的基于拓扑导数的灵敏度分析扩展到计算各向异性材料的离散变量灵敏度，其中公式的准确性通过有限差分计算来验证。单元刚度属性通过 LP 进行描述，LP 首次与离散变量拓扑优化一起使用。具体来说，采用层压参数插值法 （LPIM） 来显着减少设计变量的数量，同时确保整个层压板中纤维角度的平滑变化。此外，与以前基于 LPIM 的工作仅涉及 LP 插值主点的工作不同，引入了主线的概念以扩大刚度分布的设计空间。元素密度和 LP 经过迭代优化，以避免直接求解混合整数规划问题。通过各种案例研究证明了所开发方法的有效性，其中确定了在特定位置提供最小柔度或最大定向位移的设计。结果表明，所提出的方法可以有效地提供具有清晰密度分布和可制造纤维路径的最优可变刚度层压板设计。