A Numerical Solution of Three-Dimensional Problems in Dynamic Elasticity

[+] Author and Article Information
W. W. Recker

State University of New York at Buffalo, Buffalo, N. Y.

J. Appl. Mech 37(1), 116-122 (Mar 01, 1970) (7 pages) doi:10.1115/1.3408418 History: Received February 26, 1969; Revised April 22, 1969; Online July 12, 2010


The equations governing the dynamic deformation of an elastic solid are considered as a symmetric hyperbolic system of linear first-order partial-differential equations. The characteristic properties of the system are determined and a numerical method for obtaining the solution of mixed initial and boundary-value problems in elastodynamics is presented. The method, based on approximate integral relations along bicharacteristics, is an extension of the method proposed by Clifton for plane problems in dynamic elasticity and provides a system of difference equations, with second-order accuracy, for the explicit determination of the solution. Application of the method to a problem which has a known solution provides numerical evidence of the convergence and stability of the method.

Copyright © 1970 by ASME
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