On the thermal aspect of dynamic contact problems
A short survey of available existence results for dynamic contact problems including heat generation and heat transfer is presented.
One-dimensional model describing the non-linear viscoelastic response of materials
In this paper we consider a model of a one-dimensional body where strain depends on the history of stress. We show local existence for large data and global existence for small data of classical solutions and convergence of the displacement, strain and stress to zero for time going to infinity.
Optimal control for a class of mechanical thermoviscoelastic frictional contact problems
Quasistatic evolution in the theory of perfect elasto-plastic plates. Part II : regularity of bending moments
Quasistatic evolution of damage in an elastic-viscoplastic material.
Reissner-Mindlin plate theory for elastodynamics.
Small vertical vibrations of strings with moving ends.
In this work we investigate a mathematical model for small vertical vibrations of a stretched string when the ends vary with the time t and the cross sections of the string is variable and the density of the material is also variable, that is, p=p(x). It contains Kirchhoff model for fixed ends. We obtain solutions by Galerkin method and estimates in Sobolev spaces.
Solvability of a dynamic rational contact with limited interpenetration for viscoelastic plates
Solvability of the rational contact with limited interpenetration of different kind of viscolastic 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.