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

  • L. S. D. Morley (a1)
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.

Copyright
COPYRIGHT: © Royal Aeronautical Society 1967
References
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1.Argyris, J. H. Continua and Discontinua. Matrix Methods in Structural Mechanics, AFFDL-TR-66-80, 1966.
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.
3.Clough, R. W. Finite Element Stiffness Matrices for Analysis of Plate Bending. Matrix Methods in Structural Mechanics, AFFDL-TR-66-80, 1966.
4.De Veubeke, B. Fraeijs. Special Models for Upper and Lower Bounds. Matrix Methods in Structural Mechanics, AFFDL-TR-66-80, 1966.
5.Southwell, R. V.On the Analogues Relating Flexure and Extension of Flat Plates. Q J Mech Appl Math, Vol 3, p 257, 1950.
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.
7.Fung, Y. C.Bending of Thin Elastic Plates of Variable Thickness. J Aero Sci, Vol 20, p 455, 1953.
8.Morley, L. S. D.Some Variational Principles in Plate Bending Problems. Q J Mech Appl Math, Vol 19, p 371, 1966.
9.De Veubeke, B. Fraeijs. Displacement and Equilibrium Models in the Finite Element Method. Stress Analysis, Wiley, 1965.
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.
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The Aeronautical Journal
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