Geodesic
A contact problem for a~viscoelastic plate and an elastic beam
Sibirskij žurnal industrialʹnoj matematiki, Tome 19 (2016) no. 3, pp. 41-54

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We consider the problem of contact of a viscoelastic plate with an elastic beam. For characterizing the viscoelastic deformation of the plate, we use hereditary integrals. We present a differential statement of the problem with conditions having the form of a system of equalities and inequalities in the domain of possible contact and prove its equivalence to a variational inequality. We establish the unique solvability and the existence of the derivative of a solution with respect to time. The limit problem is considered with the parameter of bending rigidity of the plate tending to infinity.
Keywords: viscoelasticity, beam, plate, hereditary integral, variational inequality, nonpenetration condition. 
@article{SJIM_2016_19_3_a3,
     author = {T. S. Popova},
     title = {A contact problem for a~viscoelastic plate and an elastic beam},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {41--54},
     publisher = {mathdoc},
     volume = {19},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2016_19_3_a3/}
}
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T. S. Popova. A contact problem for a~viscoelastic plate and an elastic beam. Sibirskij žurnal industrialʹnoj matematiki, Tome 19 (2016) no. 3, pp. 41-54. http://geodesic.mathdoc.fr/item/SJIM_2016_19_3_a3/