Continuum Dynamics on Manifolds: Application to Elasticity of Residually-Stressed Bodies |
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Authors: | Raz Kupferman Elihu Olami Reuven Segev |
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Affiliation: | 1.Institute of Mathematics,The Hebrew University,Jerusalem,Israel;2.Department of Mechanical Engineering,Gen-Gurion University of the Negev,Beer-Sheva,Israel |
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Abstract: | This paper is concerned with the dynamics of continua on differentiable manifolds. We present a covariant derivation of the equations of motion, viewing motion as a curve in an infinite-dimensional Banach manifold of embeddings of a body manifold in a space manifold. Our main application is the motion of residually-stressed elastic bodies, where the residual stresses result from a geometric incompatibility between body and space manifolds. We then study a particular example of elastic vibrations of a two-dimensional curved annulus embedded in a sphere. |
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