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International audienceWe 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

Topics:
Korn inequality, nonlinear elasticity, elastostatics in a Riemannian manifold, Newton’s algorithm, nonlinear elliptic system, [
MATH
]
Mathematics [math], [
MATH.MATH-DG
]
Mathematics [math]/Differential Geometry [math.DG], [
MATH.MATH-AP
]
Mathematics [math]/Analysis of PDEs [math.AP], [
MATH.MATH-MP
]
Mathematics [math]/Mathematical Physics [math-ph]

Publisher: HAL CCSD

Year: 2015

OAI identifier:
oai:HAL:hal-01083499v1

Provided by:
Hal-Diderot

Downloaded from
http://hal.upmc.fr/hal-01083499/document

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