| Autor: |
Dyakonov, Radimir G., Grigor'ev, Yuri M., Popov, Sergey V., Sharin, Egor P. |
| Předmět: |
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| Zdroj: |
AIP Conference Proceedings; 2020, Vol. 2328 Issue 1, p1-4, 4p |
| Abstrakt: |
In engineering practice, the problem arises of reconstracting the stress–strain state of a structural element using the data measured on the accessible part of the it's boundary. For solving this problem in the framework of the elastic model, we have the Cauchy problem for the Lame equation. The Cauchy problem for an elliptic Lame equation is an ill-posed problem. An instability is the main difficulty for such problems. There exist numerous methods for numerical solution of such problems but few methods are known for analytical one. In this paper we present a new analytical method for the Cauchy problem for Lame equation of the elasticity theory in a rectangle wherein a missing boundary condition is recovered from a full measurement of the stresses and displacements on an accessible boundary. As a result, for the displacement components, we obtain solutions in the form of a sum of series with three regularization parameters. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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