An improved elasticity solution for the cylinder problem with axisymmetric torsionless end loading is presented. Consideration is given to the specification of arbitrary stresses on the end of a semi-infinite cylinder with a stress-free lateral surface. As is known from the literature, the solution to this problem is obtained in the form of a nonorthogonal eigenfunction expansion. Previous solutions have utilized functions biorthogonal to the eigenfunctions to generate an infinite system of linear algebraic equations for determination of the unknown expansion coefficients. However, this system of linear equations has matrices which are not diagonally dominant. Consequently, numerical instability of the calculated eigenfunction coefficients is observed when the number of equations kept before truncation is varied. This instability has an adverse effect on the convergence of the calculated end stresses. In the current paper, a new Galerkin formulation is presented which makes this system of equations diagonally dominant. This results in the precise calculation of the eigenfunction coefficients, regardless of how many equations are kept before truncation. By consideration of a numerical example, the present solution is shown to yield an accurate calculation of cylinder stresses and displacements.
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December 1981
Research Papers
A Diagonally Dominant Solution for the Cylinder End Problem
T. D. Gerhardt,
T. D. Gerhardt
USDA-Forest Service, Forest Products Laboratory, P.O. Box 5130, Madison, Wisc. 53705
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Shun Cheng
Shun Cheng
Department of Engineering Mechanics, University of Wisconsin, Madison, Wisc. 53706
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T. D. Gerhardt
USDA-Forest Service, Forest Products Laboratory, P.O. Box 5130, Madison, Wisc. 53705
Shun Cheng
Department of Engineering Mechanics, University of Wisconsin, Madison, Wisc. 53706
J. Appl. Mech. Dec 1981, 48(4): 876-880 (5 pages)
Published Online: December 1, 1981
Article history
Received:
June 1, 1980
Revised:
January 1, 1981
Online:
July 21, 2009
Citation
Gerhardt, T. D., and Cheng, S. (December 1, 1981). "A Diagonally Dominant Solution for the Cylinder End Problem." ASME. J. Appl. Mech. December 1981; 48(4): 876–880. https://doi.org/10.1115/1.3157749
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