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| Optimal Control Approach for Bilateral Elastic Contact Problem with Power-Law Friction |
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| KeyWord:Optimal control approach, multivalued equation, Clarke subdiferential, elastic materials, bilateral contact problem, normal compliance condition, Coulomb dry friction (power-law friction) |
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| Abstract: |
| We use the control variational technique to examine an elastic contact model, subject to a non-penetration condition in the normal direction and to power-law friction, proving the unique existence of the solution. This method uses optimal control theory to minimize the energy functional of the nonlinear equation. A multivalued equation $f\in \mathcal{F}y + \partial\Phi(y)$ for the displacement field describes the problem in a weak formulation, where a linear mapping is represented by $\mathcal{F}$, and the Clarke's subdifferential of the mapping $\Phi$ is indicated by $\partial\Phi$. We employ abstract existence theorems to verify the unique weak solution to the contact model. |
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