A Posteriori Estimates for Conforming Kirchhoff Plate Elements

Abstract

We derive a residual a posteriori estimator for the Kirchhoff plate bending problem. We consider the problem with a combination of clamped, simply supported and free boundary conditions subject to both distributed and concentrated (point and line) loads. Extensive numerical computations are presented to verify the functionality of the estimators.

Nitsche’s Method for the Obstacle Problem of Clamped Kirchhoff Plates

“…0,E , with V n (u h ) and M nn (u h ) denoting the jumps over interior edges of the Kirchhoff shear force and the normal moment, see [18,19] for more details.…”

A stabilised finite element method for the plate obstacle problem

“…Following [17], see also [19], we let ω E = K 1 ∪K 2 and define an auxiliary function w = p 1 p 2 p 3 in such a way that…”

“…∂ ω E and equals to one at the midpoint of E; p 3 is the linear polynomial that is zero on E and satisfies ∂ p 3 ∂ n E = 1. Outside of ω E , w is extended by zero, see [19] for more details. From the construction of w and formula (3.20), it follows that…”

Equilibrium of Two-Dimensional Cycloidal Pantographic Metamaterials in Three-Dimensional Deformations

“…Afterwards, the program evaluated the related weak form of the equilibrium equations together with its finite-element implementation. To deal with the particular problem at hand, which entailed the presence of second derivatives of the unknown kinematical variables sought for, we used Argyris finite elements [63,64], which are C 1 /H 2 -conforming. Indeed, the related shape functions were particular Hermite quintic polynomials defined over a triangular element with 21 degrees of freedom.…”