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

Published online by Cambridge University Press:  04 July 2016

L. S. D. Morley
L. S. D. Morley*
Affiliation:
Royal Aircraft Establishment, Farnborough
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Extract

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.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 71 , Issue 682 , October 1967 , pp. 715 - 719
Copyright
Copyright © Royal Aeronautical Society 1967

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References

1.Argyris, J. H. Continua and Discontinua. Matrix Methods in Structural Mechanics, AFFDL-TR-66-80, 1966.Google Scholar
2.Bazeley, G. P., Cheung, Y. K., Irons, B. M., ZIENKIE-WICZ, O. C. Triangular Elements in Plate Bending— Conforming and Non-conforming Solutions. Matrix Methods in Structural Mechanics, AFFDL-TR-66-80, 1966.Google Scholar
3.Clough, R. W. Finite Element Stiffness Matrices for Analysis of Plate Bending. Matrix Methods in Structural Mechanics, AFFDL-TR-66-80, 1966.Google Scholar
4.De Veubeke, B. Fraeijs. Special Models for Upper and Lower Bounds. Matrix Methods in Structural Mechanics, AFFDL-TR-66-80, 1966.Google Scholar
5.Southwell, R. V.On the Analogues Relating Flexure and Extension of Flat Plates. Q J Mech Appl Math, Vol 3, p 257, 1950.Google Scholar
6.Fox, L., Southwell, R. V.Relaxation Methods Applied to Engineering Problems. Biharmonic Analysis as Applied to the Flexure and Extension of Flat Elastic Plates. Phil Trans Roy Soc London, Ser A, Vol. 239, p 419, 1945.Google Scholar
7.Fung, Y. C.Bending of Thin Elastic Plates of Variable Thickness. J Aero Sci, Vol 20, p 455, 1953.Google Scholar
8.Morley, L. S. D.Some Variational Principles in Plate Bending Problems. Q J Mech Appl Math, Vol 19, p 371, 1966.CrossRefGoogle Scholar
9.De Veubeke, B. Fraeijs. Displacement and Equilibrium Models in the Finite Element Method. Stress Analysis, Wiley, 1965.Google Scholar
10.Argyris, J. H.Reinforced Fields of Triangular Elements with Linearly Varying Strain; Effect of Initial Strain. Roy Aero Soc, Vol 69, p 799, 1965.Google Scholar