On Saint-Venant's principle and the torsion of solids of revolution

Abstract

Although a comprehensive review of the literature on SAINT-VENANT'S principle in the linearized equilibrium theory of elastic solids would serve a useful purpose, such a survey is clearly beyond the scope of these introductory remarks. The principle was originally introduced by SAINT-VENANT in connection with, and with limitation to, the problem of extension, torsion, and flexure of slender cylindrical or prismatic beams. Renewed interest in the intriguing theoretical questions posed by SAINT-VENANT'S principle was stimulated by VON MISES [1] ,(1945), who brought into focus the vagueness of the traditional universal statements of the principle, which go back to BOUSSINESQ [2]. Guided by BOUSSINESQ'S own efforts in support of the principle, and on the basis of two specific examples, YON MISES was led to interpret and amend the conventional statements in terms of assertions concerning the order of magnitude of the stresses at interior points of an elastic body under loads that are confined to several distinct portions of its boundary. The limit process underlying these assertions refers to the contraction of the regions of load-application to fixed points of the boundary and the prevailing order of magnitude of the internal stresses depends upon the nature of the individual load resultants. A mathematical formulation and proof of von Mises' version of SAINT-VENANT'S principle was supplied later by STERNBERG [3]* (1952).

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