Seminar Series - 1999-2000

Mixed Enhanced Finite Elements For the Analysis of Thick and Thin Plates

Deepu Joseph
Dept. of Engineering Mechanics
University of Nebraska - Lincoln
Advisor:  Prof. Reinhard E. Piltner

Date:  Wednesday, April 12 2000
Time:  2:00 p.m.
Place:  N177 Beadle Center


A plate is a flat structural element with a thickness which is small compared to the other two geometric dimensions.  The boundary of a plate consists of straight or curved lines in a plane.  Plates play an important role in the modeling of aerospace and civil engineering structures. These structures are usually analyzed by restricting the displacement field in the thickness direction leading to important theories like the Kirchhoff, Reissner-Mindlin-Hencky and higher order theories which take into account the warping of the cross-section.

The analytical solutions to models based on higher order theories are very complex for general boundary and loading conditions. Therefore, the use of numerical techniques like the finite element method is required. In this thesis, a few quadrilateral plate elements based on higher order theories are developed and compared to existing elements. One of the major problems in the finite element analysis of plate structures is the effect of ''shear locking'' as the thickness of the plate decreases.  ''Shear locking'' is a phenomenon in which the plate element becomes very stiff for thin plates and the deflection of the plate turns out to be far too small compared to the real solution. Thus useless numerical results are obtained when locking occurs. In order to avoid this difficulty, the concept of ''enhanced strains'' is utilized. It is observed that the resulting finite elements give accurate results for relatively coarse meshes.


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