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Fictitious domain method in the equilibrium problem for a Timoshenko-type plate contacting with a rigid obstacle. (Russian. English summary) Zbl 1289.74160

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.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
49J40 Variational inequalities
74K20 Plates
74R10 Brittle fracture
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