Proper Generalized Decomposition and layer-wise approach for the modeling of composite plate structures

• The Proper Generalized Decomposition is used for the analysis of composite plates.
• The displacements field is approximated as a sum of separated functions of (x, y) and z.
• An iterative process consists of computing a product of 2D and 1D functions at each iteration.
• Various mechanical tests for composite plates show the good capability of this method.
• Satisfactory results are obtained at a low computational cost when compared with LW approach.

In the framework of the design of laminated and sandwich structures, the computation of local quantities needs a layer-wise approach. But, the computational cost of such approach increases with the number of layers. In this work, the introduction of the Proper Generalized Decomposition (PGD) is presented for the layer-wise modeling of heterogeneous structures in order to reduce the number of unknowns. The displacement field is approximated as a sum of separated functions of the in-plane coordinates x,y and the transverse coordinate z. 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.After a preliminary study to show the relevance of the present approach, mechanical tests for thin to thick laminated and sandwich plates with various boundary conditions are presented. The results are compared with elasticity reference solutions.