Convergence and improvement of solid-based plate bending finite elements
Abstract
The finite element method has become the method of choice for the solution of plate bending problems. Despite the popularity of the finite element method in solving plate bending problems, typically used plate bending finite elements are not without serious drawbacks. Currently used plate bending finite elements may be separated into two broad classes: elements based upon Kirchhoff plate theory and elements based upon a specialization of a three-dimensional solid element. The Kirchhoff elements generally suffer non-conformity of the slopes along the edges between elements, this non-conformance may be eliminated only through a very complicated element formulation. The solid-based elements suffer from very slow convergence or shear locking if an exact integration scheme is used; the rate of convergence may be greatly increased through the use of reduced integration but only at the expense of introduction of zero energy modes. Two new solid-based plate bending elements are formulated using different kinematics than those used for Mindlin elements, these elements do not perform any better than the Mindlin elements. It is shown that shear locking is controlled by the order of the shape functions used to formulate the element. This explains both the superior performance of the nine node element over the four node element and the success of reduced integration. A simple five node element is formulated in an attempt to generate an improved, simple Mindlin element. The five node element shows a modest improvement over the four node element, however, the nine node exactly integrated element shows superior performance and is recommended for general analysis purposes.
Degree
Ph.D.
Advisors
Ting, Purdue University.
Subject Area
Civil engineering
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