A Boundary Element Method for Plane Anisotropic Elastic Media

[+] Author and Article Information
Kyu J. Lee

Hughes Aircraft Company, Los Angeles, CA 90009

A. K. Mal

Mechanical, Aerospace and Nuclear, Engineering Department, University of California, Los Angeles, CA 90024

J. Appl. Mech 57(3), 600-606 (Sep 01, 1990) (7 pages) doi:10.1115/1.2897065 History: Received August 23, 1988; Revised August 15, 1989; Online March 31, 2008


The general problem of plane anisotropic elastostatics is formulated in terms of a system of singular integral equations with Cauchy kernels by means of the classical stress function approach. The integral equations are represented over the image of the boundary in the complex plane and a numerical scheme is developed for their solution. The boundary curve is discretized and suitable polynomial approximations of the unknown functions in terms of the complex variable are introduced. This reduces the equations to a set of complex linear algebraic equations which can be inverted to yield the stresses in a straightforward manner. The major difference between the present technique and the previous ones is in the numerical formulation. The integral equations are discretized in the complex plane and not in terms of real variables which depend on arc length, resulting in improved accuracy in presence of strong boundary curvature.

Copyright © 1990 by The American Society of Mechanical Engineers
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