This study presents new framework in which the representative volume element (RVE) method and machine learning (ML) model are used to construct continuous anisotropic effective material properties for simultaneous design of the overall topology configuration and local fiber material layout in functionally graded composite structures. It is an alternative to the asymptotic homogenization design method (AHDM) to obtain continuous effective material property functions. While the AHDM uses the asymptotic homogenization theory (AHT) and Legendre polynomials, the RVE method calculates anisotropic effective material properties having nonlinear behavior with respect to design variables of microstructures, and it is easier to implement than AHT given the governing equations and appropriate boundary conditions. More efficient and accurate than Legendre polynomials, ML is used to build a continuous model of the RVE results required for simultaneous design of the overall topology configuration and local fiber material layout. To show the convenience and expandability of the proposed method, a 3D RVE model is also proposed through the extension of the 2D model. The proposed method is verified through 2D and 3D numerical examples to minimize structural compliance and obtained results are compared with those from the application of AHDM.

本研究提出了新框架，其中使用代表性体积元(RVE) 方法和机器学习(ML) 模型构建连续的各向异性有效材料特性，以同时设计功能梯度复合结构中的整体拓扑配置和局部纤维材料布局。它是渐近均质化设计方法（AHDM）的替代方法，可以获得连续有效的材料特性函数。AHDM 使用渐近均匀化理论 (AHT) 和勒让德多项式，而 RVE 方法计算具有非线性行为的各向异性有效材料属性关于微观结构的设计变量，在给定控制方程和适当的边界条件的情况下，它比 AHT 更容易实现。ML 比勒让德多项式更高效、更准确，用于构建同时设计整体拓扑结构和局部纤维材料布局所需的 RVE 结果的连续模型。为了显示所提出方法的便利性和可扩展性，还通过2D模型的扩展提出了3D RVE模型。所提出的方法通过 2D 和 3D 数值示例进行验证，以最大限度地减少结构柔顺性，并将获得的结果与应用 AHDM 的结果进行比较。