Journal of Mathematical Sciences

, Volume 195, Issue 6, pp 815–826 | Cite as

Existence of an Extremal Crack Shape in the Equilibrium Problem for the Timoshenko Plate

  • N. P. Lazarev

We consider the variational problem of equilibrium of an elastic plate (the Timoshenko model) containing a crack. On the curve describing the crack, we impose boundary conditions in the form of inequalities. We study the dependence of the solutions on the curve shape. We prove the existence of an extremal curve shape and show that the solutions weakly converge in the Sobolev space as the parameter describing the crack shape tends to zero. The convergence is strong if the external forces satisfy the Lipschitz condition. Bibliography: 19 titles. Illustrations: 1 figure.


Variational Inequality Equilibrium Problem Strong Convergence Elastic Plate Normal Cross Section 
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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Lavrent’ev Institute of Hydrodynamics SB RASNovosibirskRussia

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