Differentiation of the energy functional in the equilibrium problem for a Timoshenko plate containing a crack

The variational formulation of the equilibrium problem for a Timoshenko plate containing a vertical plane crack is considered. Nonpenetration conditions in the form of inequalities (Signorini type conditions) are specified on the crack faces. The behavior of the solution and the corresponding energy...

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Bibliographic Details
Published in:Journal of applied mechanics and technical physics 2012-03, Vol.53 (2), p.299-307
Main Author: Lazarev, N. P.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Classical and Continuum Physics
Classical Mechanics
Fluid- and Aerodynamics
Mathematical Modeling and Industrial Mathematics
Mechanical Engineering
Physics
Physics and Astronomy
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Summary:The variational formulation of the equilibrium problem for a Timoshenko plate containing a vertical plane crack is considered. Nonpenetration conditions in the form of inequalities (Signorini type conditions) are specified on the crack faces. The behavior of the solution and the corresponding energy functional of the plate with variation in the crack length is analyzed. A formula for the derivative of the energy functional along the crack length is obtained. The solutions are found to continuously depend on the parameter characterizing the crack length.
ISSN:0021-8944
1573-8620
DOI:10.1134/S0021894412020198