Shell finite element based on the Proper Generalized Decomposition for the modeling of cylindrical composite structures

• A finite element based on the Proper Generalized Decomposition is presented for the analysis of cylindrical laminated shells.
• The displacement field is approximated as a sum of separated functions of in-plane coordinates and transverse coordinate.
• Mechanical tests for thin/thick and deep/shallow laminated shells show the good capability of this method.
• This finite element yields satisfactory results at a low computational cost.

The introduction of the Proper Generalized Decomposition (PGD) is presented for the layer-wise modeling of heterogeneous cylindrical shells. The displacement field is approximated as a sum of separated functions of the in-plane coordinates and the transverse coordinate. This choice yields to an iterative process that consists of solving a 2D and 1D problem successively at each iteration. In the thickness direction, a fourth-order expansion in each layer is considered. For the in-plane description, classical Finite Element method is used. The approach is assessed through mechanical tests for thin/thick and deep/shallow laminated cylindrical shells. Both convergence rate and accuracy are discussed.