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Recent Developments Concerning Saint-Venant’s Principle: An Update

[+] Author and Article Information
Cornelius O. Horgan

Department of Applied Mathematics and Applied Mechanics Program, University of Virginia, Charlottesville VA 22903

Appl. Mech. Rev 42(11), 295-303 (Nov 01, 1989) (9 pages) doi:10.1115/1.3152414 History: Online June 03, 2009

Abstract

The simplifications arising in elasticity theory from consideration of resultant boundary conditions instead of mathematically exact pointwise conditions have been the key to widespread application of the subject. Thus, for example, theories for strength of materials, plates, and shells rely on such relaxed boundary conditions for their development. The justification of this approximation is usually based on some form of the celebrated Saint-Venant’s principle. A comprehensive survey of contemporary research concerning Saint-Venant’s principle (covering primarily the period 1965–1981) was given by Horgan and Knowles (1983). Since that time, several developments have taken place demonstrating continued interest in understanding the ramifications of Saint-Venant’s principle from both a physical and mathematical point of view. In this article we review these developments, thus providing an update on contributions to this fundamental engineering principle.

Copyright © 1989 by American Society of Mechanical Engineers
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