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.
Original language | English |
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Pages (from-to) | 61-84 |
Number of pages | 24 |
Journal | Journal of Elasticity |
Volume | 128 |
Issue number | 1 |
DOIs | |
State | Published - 1 Jun 2017 |
Bibliographical note
Publisher Copyright:© 2017, Springer Science+Business Media Dordrecht.
Keywords
- Continuum dynamics
- Differentiable manifolds
- Kinetic energy
- Residual stress
- Riemannian metric