On Saint-Venant Compatibility and Stress Potentials in Manifolds with Boundary and Constant Sectional Curvature
Authors: 
Raz Kupferman, Roee LederAuthors Info & Claims
Pages 4625 - 4657
Abstract
We address three related problems in the theory of elasticity, formulated in the framework of double forms: the Saint-Venant compatibility condition, the existence and uniqueness of solutions for equations arising in incompatible elasticity, and the existence of stress potentials. The scope of this work is for manifolds with boundary of arbitrary dimension, having constant sectional curvature. The central analytical machinery is the regular ellipticity of a boundary-value problem for a bilaplacian operator, and its consequences, which were developed in [R. Kupferman and R. Leder, arXiv:2103.16823, 2021]. One of the novelties of this work is that stress potentials can be used in non-Euclidean geometries, and that the gauge freedom can be exploited to obtain a generalization for the biharmonic equation for the stress potential in dimensions greater than two.
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Published In
DOI:10.1137/sjmaah.54.4
Issue’s Table of Contents© 2022, Society for Industrial and Applied Mathematics.
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Society for Industrial and Applied Mathematics
United States
Publication History
Published: 01 January 2022
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