Assessment of a composite beam finite element based on the proper generalized decomposition

In this paper, a finite element based on the Proper Generalized Decomposition (PGD) is presented for the analysis of bi-dimensional laminated beams. The displacement field is approximated as a sum of separated functions of x (axial coordinate) and z (transverse coordinate). This choice yields to an iterative process that consists of computing a product of two one-dimensional functions at each iteration. The capability and the behavior of the PGD approach are shown on isotropic beam with different slenderness ratios. A second and fourth-order expansion with respect to the thickness are considered. Mechanical tests for thin/thick laminated and sandwich beams are presented in order to evaluate the two approaches. They are compared with elasticity and 2D finite element reference solutions.