A simple recovery post-processing of stresses and displacements in Reissner–Mindlin analysis of anisotropic laminated plates

• Published in: Composite structures 2024-03, Vol.331, p.117894, Article 117894
• Main Authors: Mendonça, P.T.R., de Lemos, W.R.
• Format: Article
• Language: English
• Subjects: Displacement components recovery; First order shear deformation theory; Generalized finite element method; Laminated composite plates; Transverse normal stresses recovery; Transverse shear stresses recovery
• ISSN: 0263-8223; 1879-1085
• DOI: 10.1016/j.compstruct.2024.117894

The bending problem of anisotropic laminated plates is considered, modeled with first order shear deformation (FSDT) kinematic model and approximations obtained from the Generalized Finite Element Method (GFEM/ XFEM). A procedure is developed to recover the transverse normal and shear stresses and all displacement components, with improved variations across the laminate thickness, generating a complete three-dimensional approximate solution of the problem. The procedure starts with the results issuing from direct computations of in-plane stresses and displacements obtained by the 2D kinematic and constitutive equations. The recovered fields are obtained to, approximately, enforce local equilibrium, constitutive and strain–displacement equations in their three-dimensional forms, and interlaminar continuity. The general procedure considers inertia forces and von Kármán non-linearity. Corrections are made to impose the necessary 3D boundary conditions in both faces of the laminate. The easy way the GFEM admits basis function enrichment, whether by singular, discontinuous or by higher order p-enrichment, on a fixed mesh, makes the entire recovery procedure straightforward and non-iterative. The recovered fields accuracy is demonstrated in standard problems against exact solutions from three-dimensional elasticity and FEM reference approximations. Up to the author’s knowledge, the presented strategy is novel in the published literature of non-iterative post-processing methods. It provides a simple mean to obtain all stress and displacement component approximations necessary to application in many complete 3D local failure theories. •Recovery of transverse shear and normal stresses and all displacement components.•Post-processing for symmetric and asymmetric laminates and sandwiches.•Post-processing in linear and non-linear plate and shell bending problems.•Corrections for natural boundary conditions (BC) on top face of the laminate•Rule to identify a priori if the integrated stresses will satisfy the natural (BC)•Simple, non iterative, one step procedure.