On the effects of using curved elements in the approximation of the Reissner--Mindlin plate by the p version of the finite element method

Authors:
Jason Kurtz;Christos Xenophontos
Affiliations:
Division of Mathematics and Computer Science, Clarkson University, Potsdam, NY;Department of Mathematical Sciences, Loyola College, 4501 N. Charles Street, Baltimore, MD
Venue:
Applied Numerical Mathematics
Year:
2003

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Abstract

We consider the approximation of the Reissner-Mindlin plate model by the standard Galerkin p version finite element method. Under the assumption of sufficient smoothness on the solution, we illustrate that the method is asymptotically free of locking even when certain curvilinear elements are used. The amount of preasymptotic locking is also identified and is shown to depend on the element mappings. We identify which mappings will result in asymptotically locking free methods and through numerical computations we verify the results for various mappings used in practice.