Collocation and Eigenfunctions in Plane Elastostatics

by Harry D. Knostman,
Isadore K. Silverman,

Serial Information: Journal of the Engineering Mechanics Division, 1968, Vol. 94, Issue 3, Pg. 797-810

Document Type: Journal Paper


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.

Subject Headings: Load factors | Boundary conditions | Numerical methods | Elastic analysis | Computing in civil engineering | Homogeneity | Convergence (mathematics) | Arbitration

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