Geodesic
Equilibrium problem for a Timoshenko plate contacting by its lateral surface along a strip of a given width
Čelâbinskij fiziko-matematičeskij žurnal, Tome 9 (2024) no. 4, pp. 596-608

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A new model of a transversally isotropic Timoshenko plate is justified, which may come into contact by its side surface with a non-deformable obstacle along a strip of a given width. The non-deformable obstacle restricts displacements and rotation angles of the plate along the outer side edge. The obstacle is defined by a cylindrical surface, the generatrices of which are perpendicular to the middle plane of the plate. A problem is formulated in variational form. A set of admissible displacements is specified in a suitable Sobolev space in the framework of a clamping condition and a non-penetration condition. The non-penetration condition is given as a system of two inequalities. The existence and uniqueness of a solution to the problem is proven. An equivalent differential formulation is found under the assumption of additional regularity of the solution to the variational problem. A qualitative connection has been established between the proposed model and a previously studied problem in which the plate is in contact over the entire side surface.
Keywords: contact problem, limit passage, variational inequality, nonpenetration condition. 
@article{CHFMJ_2024_9_4_a5,
     author = {N. P. Lazarev and D. Ya. Nikiforov and N. A. Romanova},
     title = {Equilibrium problem for a {Timoshenko} plate contacting by its lateral surface along a strip of a given width},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {596--608},
     publisher = {mathdoc},
     volume = {9},
     number = {4},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2024_9_4_a5/}
}
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N. P. Lazarev; D. Ya. Nikiforov; N. A. Romanova. Equilibrium problem for a Timoshenko plate contacting by its lateral surface along a strip of a given width. Čelâbinskij fiziko-matematičeskij žurnal, Tome 9 (2024) no. 4, pp. 596-608. http://geodesic.mathdoc.fr/item/CHFMJ_2024_9_4_a5/