Load symmetry and energy minimization in Saint-Venant's problem
type: Item
instance of: scholarly article
title: Load symmetry and energy minimization in Saint-Venant's problem
zbMATH Open document ID: 0657.73004
DOI: 10.1016/0093-6413(87)90060-7
author: P. Podio-Guidugli
published in: Mechanics Research Communications
publication date: 1987-01-01T00:00:00Z
review text: Saint-Venant's solution, if regarded as the solution of an elastic three- dimensional problem, is not necessarily unique, since tractions on the bases are not locally specified, but only their resultants are given. To overcome this indeterminateness Saint-Venant himself imposed the further condition that three stress components \((\sigma_{xx},\sigma_{yy},\sigma_{xy})\) are identically zero. Since this condition may appear artificial, it has been tried, in more recent times, to justify this assumption more rationally. \textit{J. K. Knowles} and \textit{E. Sternberg} [Arch. Ration. Mech. Anal. 22, 100-120 (1966; Zbl 0149.434)] proved that Saint-Venant's solutions have the peculiar property of minimizing the strain energy when tractions on the bases satisfy a certain local condition of equilibrium, but this does not happen when, for instance, the characteristics of displacement, instead of stress, on the bases are prescribed. It is thus convenient to enlarge the class introduced by Knowles and Sternberg, and the suitable choice is that of elastic states obeying a certain condition of global equilibrium at the bases.
reviewed by: Piero Villaggio
Mathematics Subject Classification ID: 74G50
Mathematics Subject Classification ID: 74S30
zbMATH DE Number: 4074590
zbMATH Keywords: Saint-Venant's semi-inverse method
zbMATH Keywords: peculiar end load symmetries
zbMATH Keywords: energy minimizers
MaRDI profile type: Publication
full work available at URL: 0093-6413(87)90060-7
OpenAlex ID: W2069550100
Recommended article: Q3836299
Recommended article: Q4427955
Recommended article: Sur le problème de torsion et de flexion des poutres élastiques composées.
Recommended article: Un criterio di scelta tra soluzioni elastiche a risultanti eguali.
Recommended article: Q3485924
Recommended article: Q5294471
Recommended article: Q4394661
Recommended article: Q3833696
Recommended article: Saint-Venant's problem
Recommended article: Généralisations du problème de Saint-Venant.
description: scientific article; zbMATH DE number 4074590