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On unilaterally supported viscoelastic von Kármán plates with a long memory

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  • Bock, Igor
  • Lovíšek, Ján

Abstract

We deal with the system consisting of the nonlinear integro-differential variational inequality for the deflection and the nonlinear quasistationary equation for the Airy stress function. The system describes moderately large deflections with an inner obstacle of a thin viscoelastic plate made of a long memory material. The corresponding Volterra type canonical integro-differential variational inequality is solved using a semidiscrete approximation transforming the problem into the sequence of stationary variational inequalities of von Kármán type. The existence of a solution as well as the convergence of a semidiscrete approximation to a solution of the Volterra variational inequality with a nonlinear main part are verified.

Suggested Citation

  • Bock, Igor & Lovíšek, Ján, 2003. "On unilaterally supported viscoelastic von Kármán plates with a long memory," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 61(3), pages 399-407.
    • Handle: RePEc:eee:matcom:v:61:y:2003:i:3:p:399-407
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