Stresses at the Intersection of Sphere and Cylinder by a Variant Finite-Difference Method

[+] Author and Article Information
Mustafa Hassan Fayed

Department of Mathematics and Physics, University of Alexandria, El Hadara, Alexandria, Egypt

J. Appl. Mech 41(3), 744-752 (Sep 01, 1974) (9 pages) doi:10.1115/1.3423382 History: Received March 01, 1973; Revised December 01, 1973; Online July 12, 2010


The aim of this paper is the determination of stresses at the intersection of cylinder with the sphere using a variant finite-difference technique. Mesh lines are drawn on the cross section of the body which are roughly parallel and perpendicular to the boundary, and which the author calls natural meshes. Discretization of the governing differential equations must be carried out to reduce the continuous problem to a discrete problem, this discretization converts the problem into a set of linear simultaneous equations for the functions under consideration at a set of mesh points. The derivatives to be inserted in the governing equations and boundary conditions are found by writing Taylor series expansions at a point in terms of five neighboring points in the case where the point is an internal point (four for a boundary point). By an elimination process the derivatives can be eliminated for each point, and we are left with the unknown functions only.

Copyright © 1974 by ASME
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