Lazarev, N. P. Fictitious domain method in the equilibrium problem for a Timoshenko-type plate contacting with a rigid obstacle. (Russian. English summary) Zbl 1289.74160 Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform. 13, No. 1, 91-104 (2013). Summary: 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 inequality type describing the non-penetration of opposite crack edges. Equivalent differential formulations of the problems are found. Cited in 3 Documents MSC: 74S05 Finite element methods applied to problems in solid mechanics 49J40 Variational inequalities 74K20 Plates 74R10 Brittle fracture Keywords:Signorini boundary condition; fictitious domain; mutual non-penetration condition; Timoshenko-type plate; crack PDFBibTeX XMLCite \textit{N. P. Lazarev}, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform. 13, No. 1, 91--104 (2013; Zbl 1289.74160)