Composite beam finite element based on the Proper Generalized Decomposition

In this paper, a finite element based on the Proper Generalized Decomposition is presented for the analysis of bi-dimensional laminated beams. We propose to approximate the displacement field 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 one-dimensional functions at each iteration. Mechanical tests for thin/thick laminated and sandwich beams are presented in order to evaluate the capability of this method. Both convergence rate and accuracy are discussed. The influence of the numerical layers is also assessed.