Comparison of different degenerated approaches for the modeling of composite shell structures

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.