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

Abstract : 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 sepa-rated functions of x (axial coordinate) and z (transverse coordinate). This choice yields to an iterative pro-cess 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.
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P. Vidal, L. Gallimard, O. Polit. Assessment of a composite beam finite element based on the proper generalized decomposition. Composite Structures, Elsevier, 2012, 94 (5), pp.1900-1910. ⟨10.1016/j.compstruct.2011.12.016⟩. ⟨hal-01366922⟩

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