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

Abstract

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.