On Saint-Venant's principle in plane anisotropic elasticity

Saint-Venant's principle in linear elasticity with microstructure

Toupin's version of the Saint-Venant principle in linear elasticity is generalized to the case of linear elasticity with mierostructure. That is, it is shown that, for a straight prismatic bar made of an isotropic linear elastic material with rnicrostructure and loaded by a self-equilibrated force system at one end only, the strain energy stored in the portion of the bar which is beyond a dista...

An Energy Estimate for the Biharmonic Equation and Its Application to Saint-venant’s Principle in Plane Elastostatics

Among the many relatively recent studies of the issue known in the theory of elasticity as Saint-Venant's principle, several have been devoted to the construction of certain kinds of energy inequalities for the biharmonic differential equation in plane domains*. Such inequalities are designed to estimate the spatial rate of decay of stored energy away from a portion of the boundary which carrie...

On Saint-venant's Principle in Dynamic Linear Viscoelasticity

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 for a Micropolar Helical Body

The analog of Toupin's version of Saint-Venant's principle is proved for an isotropie, linear elastic mieropolar body of arbitrary length and of uniform cross-section which in the unstressed state is helical. That is, when such a body is loaded by self-equilibrated stresses and couple stresses at one end only, we show that the elastic strain energy stored in the part of the body beyond a certai...