Periodic elastic states: nontrivial body forces and exponentially decreasing asymptotic behavior
✍ Scribed by Kenneth B. Howell
- Publisher
- Springer Netherlands
- Year
- 1987
- Tongue
- English
- Weight
- 695 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0374-3535
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✦ Synopsis
Solutions to periodic boundary value problems involving nontrivial body forces on bodies containing the upper half plane or space are examined. It is shown that, corresponding to each periodic strain solution, there is a relatively simple and easily computed asymptotic state. It is further shown that the error in using this asymptotic state rather than the actual solution decreases exponentially with the distance from the boundary.
Implications of this behavior with regard to such topics as Saint Venant's principle, the theorem of work and energy, the uniqueness of solutions to periodic and non-periodic boundary value problems are also briefly discussed.