TWO THEOREMS ON SAINT-VENANT'S PRINCIPLE IN DISCRETE STRUCTURAL MODEL

On Saint Venant's Principle

The so-called principle of statically equivalent loads, due to Saint Venant, has been referred to for the last fifty years in almost all texts on elasticity. The statements in different books vary only slightly. Let us quote A. E. H. Love's Treatise on the mathematical theory of elasticity (4th éd., p. 132) : "According to this principle the strains that are produced in a body by the applicatio...

Saint-Venant's Principle in Linear Piezoelectricity

Toupin's version of Saint-Venant's principle in linear elasticity is generalized to the case of linear piezoelectricity. That is, it is shown that, for a straight prismatic bar made of a linear piezoelectric material and loaded by a self-equilibrated system at one end only, the internal energy stored in the portion of the bar which is beyond a distance s from the loaded end decreases exponentia...

On Saint-venant's Principle in Dynamic Linear Viscoelasticity

On Saint-Venant s principle in the two-dimensional flexural vibrations of elastic beams

In this paper we apply the method proposed in our previous paper [Int. J. Solids Struct. 40(13–14) (2003) 3293] to quantitatively estimate the violation of Saint-Venant s principle in the problem of flexural vibration of a two-dimensional strip. A probabilistic approach is used to determine the relative magnitude of the penetrating stress state and the results of computations are presented as a...

On Saint-Venant's principle in plane anisotropic elasticity

RI~SUMt~ Par une mdthode applicable ~t un tr~s grand nombre de milieu anisotropique, l'auteur utilise les in6galit6s concern~nt la d~croissance de l'6nergie darts le cas d'un probl~me plan et dans l'hypoth6se de conditions 61astostatiques lin~ahes, l'auteur pr6cise la validit6 du principe de Saint-Venant dans le cadre de ses applications. Une limite in fdrieure (en fonction des constantes 61ast...