A Generalized Method of Rotational Superposition for Problems With Elliptical Distribution of Boundary Values

[+] Author and Article Information
Gwolong Lai

Department of Construction Engineering, National Yunlin Institute of Technology, Yunlin, Taiwan 640, R.O.C.

A. R. Robinson

Department of Civil Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801

J. Appl. Mech 63(4), 911-918 (Dec 01, 1996) (8 pages) doi:10.1115/1.2787246 History: Received May 11, 1994; Revised March 21, 1996; Online October 26, 2007


An extension of the usual rotational superposition is developed from geometrical considerations. This approach relates the solution of any dynamic or static elasticity problem which corresponds to boundary values on a circular area to the solution of the problem in which the same boundary values are “stretched” in one direction. From the two-dimensional problems that correspond by rotational superposition to the circular case, new two-dimensional problems are formulated which, when super-posed properly, result in the solution for the elliptical boundary distribution. This new technique is first presented for stretching the boundary values of axially symmetric problems, and then extended to others, including the elliptical shear dislocation problem.

Copyright © 1996 by The American Society of Mechanical Engineers
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