In this paper, different degenerated shell approaches in conjunction with a layer-wise (LW) model for composite structures are investigated using Finite Element method. The first one involves a classical LW model. The second one is based on a variable separation method, the Proper Generalized Decomposition (PGD), in which the displacement field is approximated as a sum of separated functions of the in-plane coordinates and the transverse coordinate. This choice yields to a non-linear problem to be solved. An iterative process consisting of solving a 2D and 1D problem successively at each iteration is carried out. For the two approaches, a fourth-order expansion in the thickness direction is considered in each layer. For the in-plane description, classical shell Finite Element is used. These simplified approaches are assessed through mechanical tests for thin/thick and deep/shallow laminated shells with different boundary conditions. Various numbers of layers are also considered. The capabilities and limitations of the methods are discussed. The results are compared with an approach based on an exact geometry description.

在本文中，使用有限元方法研究了不同的简并壳方法以及层状（LW）模型用于复合结构。第一个涉及经典的LW模型。第二种方法基于可变分离方法，即适当的广义分解（PGD），其中位移场近似为平面内坐标和横向坐标的分离函数之和。这种选择产生了要解决的非线性问题。进行一个迭代过程，该过程包括在每次迭代中依次解决2D和1D问题。对于这两种方法，在每一层中都考虑了沿厚度方向的四阶扩展。对于平面内描述，使用经典壳有限元。通过对具有不同边界条件的薄/厚和深/浅层压壳进行机械测试，可以评估这些简化方法。还考虑了各种数量的层。讨论了方法的功能和局限性。将结果与基于精确几何描述的方法进行比较。