On Saint Venant’s Principle: Elastic Shells and Plates

[+] Author and Article Information
P. M. Naghdi

University of California, Berkeley, Calif.

J. Appl. Mech 27(3), 417-422 (Sep 01, 1960) (6 pages) doi:10.1115/1.3644017 History: Received April 27, 1959; Online September 16, 2011


This investigation is concerned with an examination of the validity of Saint Venant’s principle in the theory of thin elastic shells and plates. With the aid of an integral formula derived for the displacements and their relevant partial derivatives of all orders at a fixed point of the shell middle surface, the conclusions reached may be roughly stated as follows: If the loads acting on the shell maintained in equilibrium are purely edge loads, then the orders of magnitude of the displacements and stresses are in accord with the traditional statement of Saint Venant’s principle. On the other hand, if the loads on the shell are purely surface loads, then the conclusions concerning the orders of magnitude of the displacements and stresses are the same as those of the modified Saint Venant principle.

Copyright © 1960 by ASME
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