Accurate Evaluation of Interlaminar Stresses in Composite Laminates via Mixed One-Dimensional Formulation

Abstract

This paper presents a novel mixed one-dimensional formulation based upon Reissner’s mixed variational theorem for the accurate stress analysis of general multilayered beam problems. Carrera’s unified formulation is recalled to generate a class of theory of structure that assumes both displacements and stresses over the cross section of the beam. On the other hand, the finite element method is employed to obtain the governing equations in weak form using standard Lagrangian interpolation. Independent assumptions are taken for each layer of the laminated beam through a layerwise distribution of the unknowns, and the interlaminar continuity of the transverse stresses is imposed a priori by ensuring piecewise continuous fields in the thickness direction. A set of locally defined, hierarchical Legendre polynomials is chosen for the expansion of the variables over the cross-section surface, enabling the user to refine the model in particular zones of interest and to control the accuracy of the stress analysis through the polynomial order of the theory of structure. The numerical assessment of the proposed mixed elements for multilayered problems is carried out by comparison against benchmark solutions of the literature, including plate formulations and elasticity solutions. The free-edge problem is also addressed to show the three-dimensional capabilities of the model.