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Solvability of a dynamic rational contact with limited interpenetration for viscoelastic plates. (English) Zbl 07177871

Summary: Solvability of the rational contact with limited interpenetration of different kind of viscoelastic plates is proved. The biharmonic plates, von Kármán plates, Reissner-Mindlin plates, and full von Kármán systems are treated. The viscoelasticity can have the classical (“short memory”) form or the form of a certain singular memory. For all models some convergence of the solutions to the solutions of the Signorini contact is proved provided the thickness of the interpenetration tends to zero.

MSC:

35Q74 PDEs in connection with mechanics of deformable solids
74D10 Nonlinear constitutive equations for materials with memory
74H20 Existence of solutions of dynamical problems in solid mechanics
74K20 Plates
74M15 Contact in solid mechanics
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