Abstract. In this work we present new numerical methods to simulate the mechanics of head-tape magnetic storage devices. The elastohydrodynamic problem is formulated in terms of a coupled system which is governed by a nonlinear compressible Reynolds equation for the air pressure over the head, and a rod model for the tape displacement. A fixed point algorithm between the solutions of the elastic and hydrodynamic problems is proposed. For the nonlinear Reynolds equation, a characteristics method and a duality algorithm are developed to cope with the convection dominating and nonlinear diffusion features, respectively. Furthermore, in the duality method the convergence and optimal choice of the parameters are analyzed. At each fixed point iteration, in the elastic model a complementarity formulation is required and appropriate numerical techniques are used. For the spatial discretization different finite element spaces are chosen. Finally, numerical test examples illustrate the theoretical results, as well as the good performance in the simulation of real devices.Mathematics Subject Classification. 76A20, 76D08, 35J60, 65J15, 65N60.

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Abstract. The aim of this work is to deduce the existence of solution of a coupled problem arising in elastohydrodynamic lubrication. The lubricant pressure and concentration are modelled by Reynolds equation, jointly with the free-boundary Elrod-Adams model in order to take into account cavitation phenomena. The bearing deformation is solution of Koiter model for thin shells. The existence of solution to the variational problem presents some difficulties: the coupled character of the equations, the nonlinear multivalued operator associated to cavitation and the fact of writing the elastic and hydrodynamic equations on two different domains. In a first step, we regularize the Heaviside operator. Additional difficulty related to the different domains is circumvented by means of prolongation and restriction operators, arriving to a regularized coupled problem. This one is decoupled into elastic and hydrodynamic parts, and we prove the existence of a fixed point for the global operator. Estimations obtained for the regularized problem allow us to prove the existence of solution to the original one. Finally, a numerical method is proposed in order to simulate a real journal-bearing device and illustrate the qualitative and quantitative properties of the solution.Mathematics Subject Classification. 35R35, 74K25, 76D03, 76D08.

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