Research Article
Jun 1968
Collocation and Eigenfunctions in Plane Elastostatics
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VIEW THE REPLYPublication: Journal of the Engineering Mechanics Division
Volume 94, Issue 3
Abstract
The solution of the plane problem of classical elasticity is obtained by making use of a series of Fadle-Papkovich (or biharmonic) eigenfunctions. The biharmonic eigenfunction series is formulated for rectangular bodies which have homogeneous stress boundary conditions specified on two parallel edges. The remaining two edges are subject to self-equilibrating but otherwise arbitrary stress boundary conditions. The biharmonic stress function is developed and the equations for the stresses are presented. The method of collocation, which is well adapted for use of a digital computer, is used to determine the constants of the eigenfunction series. The method is simple, and gave good results in a number of applications. Numerical results are presented which show the accuracy of the collocation method and the convergence of the solution with an increase in the number of terms of the truncated series used. Solutions are presented for a stepped uniform load and for plates subject to loads on only one edge.
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Published In
Journal of the Engineering Mechanics Division
Volume 94 • Issue 3 • June 1968
Pages: 797 - 810
Copyright
© 1968 American Society of Civil Engineers.
History
Published in print: Jun 1968
Published online: Feb 3, 2021
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Authors
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Harry D. Knostman, M.ASCE
Asst. Prof. of Applied Mechanics, Kansas State Univ., Manhattan, Kan.
Isadore K. Silverman, M.ASCE
Lecturer, Dept. of Civ. Engrg., Univ. of Colorado, Boulder, Colo.
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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.
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