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2015 | OriginalPaper | Buchkapitel

11. Static Elasticity in a Riemannian Manifold

verfasst von : Cristinel Mardare

Erschienen in: Differential Geometry and Continuum Mechanics

Verlag: Springer International Publishing

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Abstract

We discuss the equations of elastostatics in a Riemannian manifold, which generalize those of classical elastostatics in the three-dimensional Euclidean space. Assuming that the deformation of an elastic body arising in response to given loads should minimize over a specific set of admissible deformations the total energy of the elastic body, we derive the equations of elastostatics in a Riemannian manifold first as variational equations, then as a boundary value problem. We then show that this boundary value problem possesses a solution if the loads are sufficiently small in a specific sense. The proof is constructive and provides an estimation for the size of the loads.

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Metadaten
Titel
Static Elasticity in a Riemannian Manifold
verfasst von
Cristinel Mardare
Copyright-Jahr
2015
DOI
https://doi.org/10.1007/978-3-319-18573-6_11