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), pp. 51-62.

Voir la notice de l'article provenant de la source Math-Net.Ru

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_a4,
     author = {N. P. Lazarev and M. P. Grigoryev},
     title = {Differentiation of the energy functionals for equilibrium problems of the {Kirchhoff--Love} plates with nonpenetration conditions for known configurations of plate edges},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {51--62},
     publisher = {mathdoc},
     volume = {26},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2019_26_a4/}
}
TY  - JOUR
AU  - N. P. Lazarev
AU  - M. P. Grigoryev
TI  - Differentiation of the energy functionals for equilibrium problems of the Kirchhoff--Love plates with nonpenetration conditions for known configurations of plate edges
JO  - Matematičeskie zametki SVFU
PY  - 2019
SP  - 51
EP  - 62
VL  - 26
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SVFU_2019_26_a4/
LA  - ru
ID  - SVFU_2019_26_a4
ER  - 
%0 Journal Article
%A N. P. Lazarev
%A M. P. Grigoryev
%T Differentiation of the energy functionals for equilibrium problems of the Kirchhoff--Love plates with nonpenetration conditions for known configurations of plate edges
%J Matematičeskie zametki SVFU
%D 2019
%P 51-62
%V 26
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SVFU_2019_26_a4/
%G ru
%F SVFU_2019_26_a4
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), pp. 51-62. http://geodesic.mathdoc.fr/item/SVFU_2019_26_a4/