Duality in Finite Element Methods

by Ziad M. Elias,


Serial Information: Journal of the Engineering Mechanics Division, 1968, Vol. 94, Issue 4, Pg. 931-946


Document Type: Journal Paper

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.

Subject Headings: Displacement (mechanics) | Finite element method | Plates | Bending (structural) | Stress analysis | Stress strain relations | Professional societies | Convergence (mathematics)

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