In this paper, we present a topology optimization (TO) framework to simultaneously optimize the matrix topology and fiber distribution of functionally graded continuous fiber-reinforced composites (FRC). Current approaches in density-based TO for FRC use the underlying finite element mesh both for analysis and design representation. This poses several limitations while enforcing sub-element fiber spacing and generating high-resolution continuous fibers. In contrast, we propose a mesh-independent representation based on a neural network (NN) both to capture the matrix topology and fiber distribution. The implicit NN-based representation enables geometric and material queries at a higher resolution than a mesh discretization. This leads to the accurate extraction of functionally-graded continuous fibers. Further, by integrating the finite element simulations into the NN computational framework, we can leverage automatic differentiation for end-to-end automated sensitivity analysis, i.e., we no longer need to manually derive cumbersome sensitivity expressions. We demonstrate the effectiveness and computational efficiency of the proposed method through several numerical examples involving various objective functions. We also show that the optimized continuous fiber reinforced composites can be directly fabricated at high resolution using additive manufacturing.
翻译:在本文中,我们提出了一个表层优化框架,以同时优化功能级连续纤维强化复合材料的矩阵表层和纤维分布。FRC目前采用的基于密度的方法,即对FRC采用根基有限元素网格,用于分析和设计演示。这在强制实施分元素纤维间距和生成高分辨率连续纤维的同时,造成若干限制。相反,我们提议基于神经网络的网状独立表示法,以同时捕捉矩阵表层和纤维分布。基于NNW的隐含表示法,使几何和材料查询的分辨率高于网状分解法。这导致精确提取功能级连续纤维。此外,通过将有限元素模拟纳入NNT计算框架,我们可以对端到端自动敏感度分析进行自动区分。也就是说,我们不再需要人工生成繁琐的灵敏度表达法。我们通过若干涉及各种目标功能的数字示例来证明拟议方法的有效性和计算效率。我们还表明,最佳连续纤维强化复合材料可以在高分辨率制造时直接制造。