Geodesic
Fictitious domain method in the equilibrium problem for a~Timoshenko-type plate contacting with a~rigid obstacle
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 1, pp. 91-104

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In this paper we study the nonlinear equilibrium problem for the plate with the Signorini condition on the part of the boundary. We construct a family of auxiliary problems defined in an extended domain so that their solutions converge properly to a solution of the Signorini problem. Each problem of this family describes the equilibrium of the plate with a crack. On the curve defining the crack we impose a boundary condition of an inequality type describing the non-penetration of opposite crack edges. Equivalent differential formulation of the problems is found.
Keywords: Signorini boundary conditions, fictitious domain, mutual non-penetration condition, Timoshenko-type plate, crack. 
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     author = {N. P. Lazarev},
     title = {Fictitious domain method in the equilibrium problem for {a~Timoshenko-type} plate contacting with a~rigid obstacle},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
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     publisher = {mathdoc},
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N. P. Lazarev. Fictitious domain method in the equilibrium problem for a~Timoshenko-type plate contacting with a~rigid obstacle. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 1, pp. 91-104. http://geodesic.mathdoc.fr/item/VNGU_2013_13_1_a8/