A C ^k continuous generalized finite element formulation applied to laminated Kirchhoff plate model

A generalized finite element method based on a partition of unity (POU) with smooth approximation functions is investigated in this paper for modeling laminated plates under Kirchhoff hypothesis. The shape functions are built from the product of a Shepard POU and enrichment functions. The Shepard functions have a smoothness degree directly related to the weight functions adopted for their evaluation. The weight functions at a point are built as products of C ^∞ edge functions of the distance of such a point to each of the cloud boundaries. Different edge functions are investigated to generate C ^k functions. The POU together with polynomial global enrichment functions build the approximation subspace. The formulation implemented in this paper is aimed at the general case of laminated plates composed of anisotropic layers. A detailed convergence analysis is presented and the integrability of these functions is also discussed.