A Triangular Equilibrium Element with Linearly Varying Bending Moments for Plate Bending Problems

Author:

Morley L. S. D.

Abstract

Work on the finite element analysis of flat plates in bending has been directed towards elements which satisfy kinematic conditions between the adjacent elements in conjunction with the theorem of minimum potential energy, eg Argyris, Bazeley et al, Clough and Veubeke.The purpose of this Note is to provide the main details of a triangular element which satisfies equilibrium conditions between the adjacent elements and which is used in conjunction with the complementary energy principle. The bending moments vary linearly within the element and use is made in the derivation of the analogy (see eg Southwell, Fox, Fung and Morley that exists between problems of plane stress and plate bending. In particular, many of the present details are taken directly from the plane stress analysis of Veubeke who, along with Argyris, considers a displacement triangular element with linearly varying strain.

Publisher

Cambridge University Press (CUP)

Reference10 articles.

1. Morley L. S. D. Some Variational Principles in Plate Bending Problems. Q J Mech Appl Math, Vol 19, p 371, 1966.

2. Bending of Thin Elastic Plates of Variable Thickness;Fung;J Aero Sci

3. ON THE ANALOGUES RELATING FLEXURE AND EXTENSION OF FLAT PLATES

4. Argyris J. H. Continua and Discontinua. Matrix Methods in Structural Mechanics, AFFDL-TR-66-80, 1966.

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