Geodesic
Differentiation of the energy functionals for equilibrium problems of the Kirchhoff–Love plates with nonpenetration conditions for known configurations of plate edges
Matematičeskie zametki SVFU, Tome 26 (2019) no. 4, pp. 51-62 Cet article a éte moissonné depuis la source Math-Net.Ru

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Equilibrium problems for elastic plates with a rectilinear crack are studied. It is assumed that under the action of certain given loads, plates have deformations with a certain predetermined configuration of edges near the crack. On the crack curve, we impose a nonlinear boundary condition as an inequality describing the nonpenetration of the opposite crack faces. Assuming that the parameter $\delta$ describes the crack perturbation, the derivative of the energy functional with respect to $\delta$ is found. The results are obtained for new mathematical models with new nonlinear boundary conditions describing special character of the mechanical contact interaction of the plate edges.
Keywords: variational inequality, crack, nonpenetration condition, energy functional derivative. 
@article{SVFU_2019_26_4_a4,
     author = {N. P. Lazarev and M. P. Grigoryev},
     title = {Differentiation of the energy functionals for equilibrium problems of the {Kirchhoff{\textendash}Love} plates with nonpenetration conditions for known configurations of plate edges},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {51--62},
     year = {2019},
     volume = {26},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2019_26_4_a4/}
}
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N. P. Lazarev; M. P. Grigoryev. Differentiation of the energy functionals for equilibrium problems of the Kirchhoff–Love plates with nonpenetration conditions for known configurations of plate edges. Matematičeskie zametki SVFU, Tome 26 (2019) no. 4, pp. 51-62. http://geodesic.mathdoc.fr/item/SVFU_2019_26_4_a4/