Journal ArticleDOI
Uniqueness in classical elastodynamics
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This article is published in Archive for Rational Mechanics and Analysis.The article was published on 1968-01-01. It has received 40 citations till now. The article focuses on the topics: Uniqueness.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
The Theory of Shells and Plates
TL;DR: In this paper, the authors define a shell as a 3D body whose boundary surface has special features, such as a plate and a shell-like body, which is defined by the dimension of the body along the normals, called the thickness.
Journal ArticleDOI
Some theorems in classical elastodynamics
Lewis T. Wheeler,Eli Sternberg +1 more
TL;DR: In this article, the uniqueness and reciprocal theorems of dynamic elasticity are extended to unbounded domains with the aid of a generalized energy identity and a lemma on the prolonged quiescence of the far field, which are established for this purpose.
References
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Vorlesungen über die Theorie der Elasticität der festen Körper und des Lichtäthers
Franz Neumann,Oskar Emil Meyer +1 more
Journal ArticleDOI
A note on uniqueness in classical elastodynamics
Morton E. Gurtin,Eli Sternberg +1 more
TL;DR: The uniqueness theorems of classical elasticity theory, first established by Kirchhoff [l]1 for the equilibrium case and later extended to elastodynamics by Neumann [2], rest on the assumption that the elastic constants satisfy inequalities which are necessary and sufficient for the positive definiteness of the strain energy density as discussed by the authors.
Journal ArticleDOI
A uniqueness theorem for the displacement boundary-value problem of linear elastodynamics
M. E. Gurtin,R. A. Toupin +1 more
Journal ArticleDOI
On the displacement boundary-value problem of linear elastodynamics
Michael Hayes,R. J. Knops +1 more
TL;DR: In this article, Gurtin and Toupin et al. considered the uniqueness problem of finding necessary and sufficient conditions on the cijkl so that the only twice continuously diferentiable solution of (l)-(4) is identically zero.