Analysis of anisotropic Mindlin plate model by continuous and non-continuous GFEM

This paper presents a generalized finite element formulation with arbitrarily continuous unknown fields for static bending analysis of anisotropic laminated plates based on Mindlin's kinematical model. This consist of an extension of the work of Barcellos et al. (2009) [39] to moderate thick plates and also exploits the properties of smooth approximation functions built from the Duarte extension of Edwards’ procedure (Duarte et al., 2006 [44]) in the framework of the so-called Ck-GFEM. The strategy is suitable for p- and k-enrichments on a fixed mesh of finite elements and its accuracy is evaluated in numerical experiments against analytical solutions. The performance is compared to the standard C0-GFEM/XFEM approach and several topics of concern are investigated, such as the required number of integration points for the computation of the element matrices, the influence of the degree of polynomial enrichment, the degree of inter-element continuity chosen for the basis functions, the effect of laminate thickness and the sensitivity to mesh distortions and its relation with the stiffness matrix conditioning. Errors in-plane and transverse shear stresses are computed. The smoothness contributes to the accuracy in terms of the energy norm and furnishes better derivatives of the solution fields, leading to better post-processed transverse shear stresses, which can be further improved by a proposed heuristic procedure.