Two new triangular G~1-conforming finite elements with cubic edge rotation for the analysis of Kirchhoff plates

摘要

Two triangular G(1)-conforming elements, based on the triangular Gregory patch, suitable for the analysis of the Kirchhoff plate model are presented. Both have cubic normal derivative along the sides, so that they can be effectively used in combination with generalized Hermitian elements.The Gregory patch consists in a rational enhancement of the base-polynomial spaces useful to design G(1)-conforming elements on general C-0-conforming unstructured meshes.Because of the presence of the rational functions, the second derivatives at the corners of the element present finite discontinuities, that prevent the elements from passing the bending patch test. The discontinuities are removed using a constrained version of the Gregory patch, with Lagrange multipliers. In this way, the rational conforming space collapses into a conforming rearrangement of the original polynomial interpolant spaces.The proposed formulation design elements that pass the bending patch test and present optimal rate of convergence on general unstructured meshes. (C) 2019 Elsevier B.V. All rights reserved.