Cut Bogner-Fox-Schmit elements for plates
Open Access
- 11 June 2020
- journal article
- research article
- Published by Springer Science and Business Media LLC in Advanced Modeling and Simulation in Engineering Sciences
- Vol. 7 (1), 1-20
- https://doi.org/10.1186/s40323-020-00164-3
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.
Keywords
Funding Information
- Stiftelsen för Strategisk Forskning (AM13-0029)
- Vetenskapsrådet (2013-4708, 2017-03911)
- Vetenskapsrådet (2018-05262)
- Engineering and Physical Sciences Research Council (EP/P01576X/1)
- Swedish Research Programme Essence (N/A)
This publication has 21 references indexed in Scilit:
- A family of C0 finite elements for Kirchhoff plates II: Numerical resultsComputer Methods in Applied Mechanics and Engineering, 2008
- A C0 discontinuous Galerkin formulation for Kirchhoff platesComputer Methods in Applied Mechanics and Engineering, 2007
- C 0 Interior Penalty Methods for Fourth Order Elliptic Boundary Value Problems on Polygonal DomainsJournal of Scientific Computing, 2005
- A finite element method on composite grids based on Nitsche's methodESAIM: Mathematical Modelling and Numerical Analysis, 2003
- A discontinuous Galerkin method¶for the plate equationCalcolo, 2002
- Curved finite elements of classComputer Methods in Applied Mechanics and Engineering, 1993
- On Mixed Finite Element Methods for the Reissner-Mindlin Plate ModelMathematics of Computation, 1992
- The Plate Paradox for Hard and Soft Simple SupportSIAM Journal on Mathematical Analysis, 1990
- A Uniformly Accurate Finite Element Method for the Reissner–Mindlin PlateSIAM Journal on Numerical Analysis, 1989
- Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sindAbhandlungen aus dem Mathematischen Seminar der Universitat Hamburg, 1971