Review Articles

Toupin-Type Decay and Saint-Venant’s Principle

[+] Author and Article Information
Jian-Zhong Zhao

 Geophysics Department, College of Resource, Environment and Earth Sciences, Yunnan University, Kunming, Yunnan, Chinajzhzhaokm@yahoo.com.cn

Appl. Mech. Rev 63(6), 060803 (Jun 28, 2011) (20 pages) doi:10.1115/1.4004008 History: Received December 26, 2008; Accepted April 14, 2011; Revised April 14, 2011; Published June 27, 2011; Online June 28, 2011

Toupin’s Theorem plays the most influential role in the history of development concerning Saint-Venant’s Principle. We now review the history and the previous works, distinguishing Saint-Venant type decay from Toupin-type decay and arguing that Toupin’s Theorem is not a formulation of Saint-Venant’s Principle; Saint-Venant’s Principle stated by Love can be disproved mathematically from Toupin’s Theorem, so Toupin’s Theorem is mathematically inconsistent with Saint-Venant’s Principle; Modified Saint-Venant’s Principle can be proved or formulated, though Saint-Venant’s Principle in its general form stated by Boussinesq and Love is not true.

Copyright © 2011 by American Society of Mechanical Engineers
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