This paper presents a hierarchic finite element-based computational framework for the multi-scale modelling of composite laminates. Hierarchic finite elements allow changing the approximation order locally or globally without changing the underlying finite element mesh. Both micro- and macro-level structures are discretised with these elements. The macro-level structures of composite laminates are divided into several blocks during the pre-processing stage, and approximation orders are assigned to each block independently. Due to a sharp increase in the interlaminar stresses, higher approximation orders are used in the vicinity of free edges as compared to the rest of the problem domain. This freedom of assigning approximation orders independently to each block provides an efficient and accurate way for modelling composite laminates. The computation framework can either accept the user-defined ply-level homogenised elastic material properties or calculates these directly from the underlying representative volume element consisting of matrix and fibre using the computational homogenisation. The model developed for the computational homogenisation has the flexibility of unified imposition of representative volume element boundary conditions, which allows convenient switching between linear displacement, uniform traction and periodic boundary conditions. The computational framework has additional flexibly of high-performance computing and makes use of state-of-the-art computational libraries including Portable, Extensible Toolkit for Scientific Computation (PETSc) and the Mesh-Oriented datABase (MOAB). Symmetric cross-ply, angle-ply and quasi-isotropic laminates subjected to uniaxial loading are used as test cases to demonstrate the correct implementation and computational efficiency of the developed computational framework.

本文提出了一种基于层次有限元的计算框架，用于复合材料层压板的多尺度建模。分层有限元允许局部或全局更改近似顺序，而无需更改基础有限元网格。这些元素离散了微观和宏观结构。复合材料层压板的宏观结构在预处理阶段分为几个块，并且分别将近似顺序分配给每个块。由于层间应力急剧增加，因此与问题域的其余部分相比，在自由边缘附近使用了更高的近似阶数。独立为每个块分配近似顺序的这种自由性为复合材料层压板的建模提供了一种有效而准确的方法。计算框架可以接受用户定义的层级均质化弹性材料属性，也可以使用计算均质化直接从由基质和纤维组成的基础代表性体积元素中计算出这些值。为计算均匀化而开发的模型具有统一施加代表性体积元素边界条件的灵活性，这允许在线性位移，均匀牵引力和周期性边界条件之间方便地进行切换。该计算框架具有高性能计算的更多灵活性，并利用了最新的计算库，包括便携式，可扩展的科学计算工具包（PETSc）和面向网格的datABase（MOAB）。对称交叉网