Generalized multifield variational formulation with interlaminar stress continuity for multilayered anisotropic beams

Abstract

Classical finite element (FE) beam theories are based on displacement formulation requiring derivatives to obtain the stress components which leads to a large number of FEs and depend on nodal averaging techniques for achieving sufficient accuracy. In this work, a new multifield variational based FE formulation is proposed within the cross-sectional framework of multilayered composite beams for accurate and efficient predictions of sectional stiffness constants and stresses. The interlaminar stress continuity is not assumed a priori and inherently incorporated using the Hellinger-Reissner principle along with a global stress equilibrium constraint, directly computing the stresses at nodal locations. The three-dimensional (3D) stresses and warping deformations are considered as primary variables which inherently incorporate elastic coupling effects related to transverse shear and Poisson deformations. The formulation results in a generalized fully-coupled 6×6 sectional stiffness matrix considering elastic couplings. The efficacy of the present analysis is substantiated for thin-walled composite beams with elastic couplings. An excellent correlation is achieved for the elastostatic response as compared with the 3D FE and experimental results. The stresses obtained by the multifield analysis are in accord with detailed 3D FE solutions for various loading conditions while computed at a much reduced computational cost. Improved predictions of interlaminar stresses and stress concentrations are achieved compared to displacement-based approach along with the correct identification of continuity across layer interfaces. The effect of fiber orientation on the interlaminar stresses is also shown to be significant which can be useful for damage analysis of composite beams.