APPLICATION OF THE GENERALIZED FINITE ELEMENT METHOD TO THE FIRST ORDER SHEAR DEFORMATION THEORY APPLIED TO ISOTROPIC AND SANDWICH PLATES UNDER LARGE DISPLACEMENTS

Resumo

This paper presents a procedure to extract accurate transverse normal and shear stresses, and
the transverse and in-plane displacements, in isotropic plates, symmetric laminated composite plates and
plates with sandwich structure, modeled by the First Order Shear Deformation Theory (FSDT), under
large displacements considered in the von Kármán sense. The Generalized Finite Element Method
(GFEM) is used, in which the enrichment of the Partition of Unity (PoU) functions is done by complete
polynomials functions, improving the obtained results, and making it possible to obtain basis of
approximate functions with degree 4 of polynomial reproducibility. This makes possible to obtain
straightforwardly the third derivatives of transverse displacement w, which is needed in most extraction
procedures based on the integration of the local equilibrium and kinematic equations. The procedure
starts with the integration of the local differential equations static equilibrium, using the results obtained
from the direct calculations of stresses and displacements by the constitutive equations using the results
of the GFEM. Modifications of the stresses at given integration points are performed to enforce the
following conditions: (a) the satisfaction of boundary conditions on both faces of the laminate, (b)
equivalence with the resultant shear forces, and (c) interlaminar continuity of stresses. The transverse

and in-plane displacements are integrated along the thickness using the three-dimensional local stress-
strain relations for anisotropic layers. The stresses and deflections calculated with the proposed post-
processing are compared with the stresses and deflections obtained in the literature or calculated using

a three-dimensional Finite Element (FEM) analysis that serves as a reference. The proposed stress
recovery procedure, when applied to geometrically nonlinear problems, generate estimates that show a
good correlation with the three-dimensional FEM reference solutions and with the solutions present in
the literature, for all test cases of isotropic, laminated plates and sandwich plates. For the displacements
along the thickness the results are satisfactory, considering that the solution comes from a first order
model.