Geodesic
The equilibrium problem for a Timoshenko plate containing a crack along a thin rigid inclusion
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2014), pp. 32-45 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the equilibrium problem of a transversely isotropic plate with rigid inclusions. It is assumed that the plate deforms under hypotheses of classical elasticity. The problems are formulated as the minimization of the plate energy functional on the convex and closed subset of the Sobolev space. It is established that, as the geometric parameter (the size) of the volume inclusion tends to zero, the solutions converge to the solution of an equilibrium problem of a plate with a thin rigid inclusion. Also the case of the delamination of an inclusion is investigated when a crack in the plate is located along one of the inclusion edges. In the problem of a plate with a delaminated inclusion the nonlinear condition of nonpenetration is given. This condition takes the form of a Signorini-type inequality and describes the mutual nonpenetration of the crack edges. For the problem with a delaminated inclusion, the equivalence of variational and differential statements is proved provided a sufficiently smooth solution. For each considered variation problem, unique solvability is established.
Keywords: crack, Timoshenko-type plate, rigid inclusion, energy functional, variational problem, nonpenetration condition. 
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N. P. Lazarev. The equilibrium problem for a Timoshenko plate containing a crack along a thin rigid inclusion. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2014), pp. 32-45. http://geodesic.mathdoc.fr/item/VUU_2014_1_a2/

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