Geodesic
On the equilibrium of a two-layer elastic structure with a crack
Sibirskij žurnal industrialʹnoj matematiki, Tome 22 (2019) no. 4, pp. 107-120

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Under study is some problem concerning the equilibrium of a two-layer structure whose layers are some elastic plates. The upper layer is glued to the lower one along a part of the edge. The behavior of the plates is modelled in the framework of the plane theory of elasticity. Along the gluing line in the lower layer, there is a crack crossing the external boundary at zero angle. On the crack faces, the nonlinear boundary conditions are imposed that exclude their mutual penetration. The solvability of the equilibrium problem is considered as well as the behavior of the solution in the case when the elasticity moduli of upper plate tend to zero or to infinity.
Keywords: two-layer structure, crack, nonpenetration condition, fictitious domain method, variational inequality. 
@article{SJIM_2019_22_4_a10,
     author = {I. V. Frankina},
     title = {On the equilibrium of a two-layer elastic structure with a crack},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {107--120},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2019_22_4_a10/}
}
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I. V. Frankina. On the equilibrium of a two-layer elastic structure with a crack. Sibirskij žurnal industrialʹnoj matematiki, Tome 22 (2019) no. 4, pp. 107-120. http://geodesic.mathdoc.fr/item/SJIM_2019_22_4_a10/