"SOME REMARKS ON THE PRINCIPLES OF SAINT-VENANT"

Abstract

"The validity of the generalized Hooke’s law is checked by the relations obtained from the solution of the boundary value problem of the equilibrium of the cylinder, the boundary conditions on the basis of which are simplified on the basis of the narrowed and general principles of Saint-Venant. However, these relations are not a generalized Hooke’s law, but the kind in which these principles are invisibly present. With this in mind, they should be called Hooke–Saint-Venant relations. In this light, the deviation of experimental data from these relations should be discussed not as a deviation from the generalized Hooke’s law, but from its simplified form by the principles of Saint-Venant. The ratios turned out to be inconsistent, the experimental points are not located in the way they envisage. This, it would seem, is the end of the question. But no, the load-strain diagram has gained independence. Based on the assumption, as shown in this paper, it began to be considered as an experimentally determined physical law. The real deformation, as shown, cannot be explained at all by expressions (4), according to which the parts of the body do not interact with each other at all. But the acceptance of this assumption has become fixed – the tense state must necessarily be uniaxial. Keywords: Saint-Venant principle, Hooke–Saint-Venant relation, Hooke’s law, deformation, mechanics of deformable body."