Research Article
Aug 1968
Duality in Finite Element Methods
Publication: Journal of the Engineering Mechanics Division
Volume 94, Issue 4
Abstract
The duality between the basic equations and the dependent variables in problems of stretching and of bending of plates is applied to the finite element method. A displacement method in the stretching problem is a stress function method in the bending problem and vice versa. The stress function method has the same properties of accuracy and convergence as the well established dual displacement method for plate stretching, using only two equations per node. A computer program, originally written for the analysis of plane stress and plane strain problems by the displacement method, is used to solve plate bending problems. Results show that a high degree of accuracy may be achieved for the stress couples. The determination of the deflection and slopes is made from the curvatures and involves no loss of accuracy. Comparisons with results of the fully compatible displacement method are presented.
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Published In
Journal of the Engineering Mechanics Division
Volume 94 • Issue 4 • August 1968
Pages: 931 - 946
Copyright
© 1968 American Society of Civil Engineers.
History
Published in print: Aug 1968
Published online: Feb 3, 2021
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Ziad M. Elias, AM.ASCE
Asst. Prof., Dept. of Civ. Engrg., Massachusetts Inst. of Tech., Cambridge, Mass.
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ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.