Robust C~k/C~0 generalized FEM approximations for higher-order conformity requirements: Application to Reddy's HSDT model for anisotropic laminated plates

摘要

The Third-order Plate Theory proposed by Reddy for modeling laminated composite plates has earned wide acceptance in the engineering community. It involves the same five generalized displacement components (u~o, v~o, w~o, ψ_x, ψ_y) as the first-order models (e.g. Mindlin's) and, at the same time, its higher-order expansion across the thickness enables it to provide more accurate displacements and layer-wise stress estimates. However, its FEM implementation is somewhat hindered by the need to employ a C~1 (Ω) continuous basis for the transverse displacement w~o. In this paper, an instance of the Generalized Finite Element Method, GFEM, which allows an arbitrary C~k continuity, is used to solve arbitrary anisotropic laminated composite plate bending problems. The resultant basis functions naturally exhibit inter-element continuity and can be easily enriched to generate arbitrary p-enriched basis functions. These characteristics result in excellent abilities in terms of approximating the layer stresses. In particular, the high degree of the basis, combined with its continuity, enables the transverse shear stresses to be integrated from the local equilibrium equations, and also post-processed in a scaling operation explored by the authors to provide additional accuracy of the estimates across the thickness. Additionally, all of the estimated strain and stress fields are naturally continuous, without the need for any heuristic averaging or smoothing operation. The procedure is robust enough to allow for Partition of Unity (Poll) construction free of geometrical restrictions on the elements and it is suitable for mixed C~k/C~o formulations, using continuous functions only for those variables which require such continuity, in order to reduce the computational cost. The method is implemented with three-node triangular elements, and its performance is illustrated through comparisons with analytic solutions, with special emphasis on the computation of the transverse stress field for thick laminates.