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Static Elasticity in a Riemannian Manifold

By Cristinel Mardare

Abstract

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

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