Geodesic
On a contact problem for a viscoelastic von Kármán plate and its semidiscretization
Applications of Mathematics, Tome 50 (2005) no. 3, pp. 203-217 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We deal with the system describing moderately large deflections of thin viscoelastic plates with an inner obstacle. In the case of a long memory the system consists of an integro-differential 4th order variational inequality for the deflection and an equation with a biharmonic left-hand side and an integro-differential right-hand side for the Airy stress function. The existence of a solution in a special case of the Dirichlet-Prony series is verified by transforming the problem into a sequence of stationary variational inequalities of von Kármán type. We derive conditions for applying the Banach fixed point theorem enabling us to solve the biharmonic variational inequalities for each time step.
We deal with the system describing moderately large deflections of thin viscoelastic plates with an inner obstacle. In the case of a long memory the system consists of an integro-differential 4th order variational inequality for the deflection and an equation with a biharmonic left-hand side and an integro-differential right-hand side for the Airy stress function. The existence of a solution in a special case of the Dirichlet-Prony series is verified by transforming the problem into a sequence of stationary variational inequalities of von Kármán type. We derive conditions for applying the Banach fixed point theorem enabling us to solve the biharmonic variational inequalities for each time step.
DOI : 10.1007/s10492-005-0014-2
Classification : 49J40, 65R20, 74D10, 74K20
Keywords: von Kármán system; viscoelastic plate; integro-differential variational inequality; semidiscretization; Banach fixed point theorem 
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     title = {On a contact problem for a viscoelastic von {K\'arm\'an} plate and its semidiscretization},
     journal = {Applications of Mathematics},
     pages = {203--217},
     year = {2005},
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Bock, Igor; Lovíšek, Ján. On a contact problem for a viscoelastic von Kármán plate and its semidiscretization. Applications of Mathematics, Tome 50 (2005) no. 3, pp. 203-217. doi: 10.1007/s10492-005-0014-2

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