Journal ArticleDOI
On Saint-Venant's principle in the two-dimensional linear theory of elasticity
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In this article, the authors provide a formulation and proof of a version of Saint-Venant's principle appropriate to the plane strain and generalized plane stress solutions of the equations of the linear theory of elastic equilibrium.Abstract:
This paper presents results which provide a formulation and proof of a version of Saint-Venant's principle appropriate to the plane strain and generalized plane stress solutions of the equations of the linear theory of elastic equilibrium.read more
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Book ChapterDOI
The Linear Theory of Elasticity
TL;DR: Linear elasticity is one of the more successful theories of mathematical physics and its pragmatic success in describing the small deformations of many materials is uncontested The origins of the three-dimensional theory go back to the beginning of the 19th century and the derivation of the basic equations by Cauchy, Navier, and Poisson The theoretical development of the subject continued at a brisk pace until the early 20th century with the work of Beltrami, Betti, Boussinesq, Kelvin, Kirchhoff, Lame, Saint-Venant, Somigl
Book ChapterDOI
Recent Developments Concerning Saint-Venant's Principle
TL;DR: In this paper, the authors provide an overview of the recent developments concerning Saint-Venant's principle and present an exact solution for the exact solution of the second-order problem.
Journal ArticleDOI
Saint-Venant's Principle
TL;DR: In this paper, the elastic equivalence of statically equivalent systems of load, or Saint-Venant's Principle, is given a precise mathematical formulation and proof. And the results are compared with previous mathematical work on the principle.
Journal ArticleDOI
Boundary-value problems for partial differential equations in non-smooth domains
V A Kondrat'ev,O A Oleinik +1 more
TL;DR: In this paper, the authors considered boundary value problems in non-smooth domains with conic points and isolated non-regular points on the boundary and showed that the solutions of these problems are asymptotic in the neighbourhood of a conic boundary point.
References
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Journal ArticleDOI
Saint-Venant's Principle
TL;DR: In this paper, the elastic equivalence of statically equivalent systems of load, or Saint-Venant's Principle, is given a precise mathematical formulation and proof. And the results are compared with previous mathematical work on the principle.
Journal ArticleDOI
On Saint Venant's principle
TL;DR: In this paper, it was shown that if the forces acting upon a body are restricted to several small parts of the surface, each included in a sphere of radius e, then the strains and stresses produced in the interior of the body at a finite distance from all those parts are smaller in order of magnitude when the forces for each single part are in equilibrium than when they are not.