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On the role of the Stokes-Helmholtz decomposition in the derivation of displacement potentials in classical elasticity

โœ Scribed by D. A. W. Pecknold

Publisher
Springer Netherlands
Year
1971
Tongue
English
Weight
140 KB
Volume
1
Category
Article
ISSN
0374-3535

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โœฆ Synopsis

General solutions of the Cauchy-Navier equations in classical elasticity are well known. Among these are the Papkovich-Neuber [1 ], [2], Galerkin , and Naghdi-Hsu [3] representations. Derivations of these systems of displacement potentials conventionally employ the Stokes-Helmholtz decomposition, or a close relative thereof, in a central role *. In this note, it is shown that the Stokes-Helmholtz decomposition per se ** is, in fact, not an essential ingredient in the derivation.

We begin by formulating the problem in terms of stresses rather than displacements. The appropriate field equations are the equilibrium equations ***

๐Ÿ“œ SIMILAR VOLUMES

On uniqueness for the displacement probl
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By means of a weighted form of Garding's inequality, we prove a uniqueness theorem for the initial boundary value problem of finite elastodynamics in unbounded domains. ## Sommario Mediante un'opportuna forma pesata della disuguaglianza di Garding, che ricaviamo preliminarmente, dimostriamo un te