A G/XFEM approximation space based on the enrichment of rational polynomials to model free and forced vibration in elastic isotropic Mindlin–Reissner plates

Abstract

The aim of this paper is to show the influence of a devised approximation space in obtaining natural frequencies, especially relatively high ones, and in the prediction of the undamped dynamic behavior produced by impulsive forces in plates. To achieve this goal, it is proposed to build an approximation space within the G/XFEM context. This space is based on the partition of unity family of rational polynomials which can, preserved some conditions under the mesh, generate shape functions of high regularity. The PU shape functions are then enriched using monomials defined on a normalized local coordinate system built at the nodes of the mesh. The proposed numerical framework is assessed by comparisons with analytical and reference (numerical) solutions, as well as with high-order $$C^{0}$$ FEM-Lagrange predictions.