Cut Bogner-Fox-Schmit Elements for Plates

TL;DR

This paper introduces a novel finite element method for thin plates using cut Bogner-Fox-Schmit elements, employing Nitsche's method and stabilization to ensure stability and accuracy, especially for simply supported boundary conditions.

Contribution

The paper develops a new approach combining cut Bogner-Fox-Schmit elements with Nitsche's method for improved plate modeling, including boundary approximation considerations.

Findings

Method achieves coercivity and stability.

Effective handling of boundary geometric approximation.

Applicable to simply supported boundary conditions.

Abstract

We present and analyze a method for thin plates based on cut Bogner-Fox-Schmit elements, which are $C^1$ elements obtained by taking tensor products of Hermite splines. The formulation is based on Nitsche's method for weak enforcement of essential boundary conditions together with addition of certain stabilization terms that enable us to establish coercivity and stability of the resulting system of linear equations. We also take geometric approximation of the boundary into account and we focus our presentation on the simply supported boundary conditions which is the most sensitive case for geometric approximation of the boundary.