Research Article
Aug 1969
Finite Element Plate Bending Equilibrium Analysis
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VIEW THE REPLYPublication: Journal of the Engineering Mechanics Division
Volume 95, Issue 4
Abstract
For the problem of elastic plate bending, a finite element procedure based on the minimum of complementary energy principle is developed. Primary variable of the problem is the distribution of the bending moments mx, my and mxy. These vary parabolically inside each triangular element and have continuous values throughout the plate. In order to satisfy the equilibrium conditions, Lagrangean multipliers are introduced as secondary variables. It is then shown that these multipliers are generalized displacement parameters. The final solution will therefore provide direct information about both the stress distribution and the displaced shape of the plate. Equilibrium conditions are satisfied exactly. A strain energy bound is found. For several cases numerical results are given and compared with known solutions.
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Published In
Journal of the Engineering Mechanics Division
Volume 95 • Issue 4 • August 1969
Pages: 841 - 857
Copyright
© 1969 American Society of Civil Engineers.
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Published in print: Aug 1969
Published online: Feb 3, 2021
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Edoardo Anderheggen
Research Assoc., Inst. for Structural Engrg. of the Swiss Federal Inst. of Technology, Zürich, Switzerland
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