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Mathematical analysis of some new Reynolds-rod elastohydrodynamic models. (English) Zbl 1068.74018
Summary: In this paper, some new elastohydrodynamic Reynolds-rod models are posed to obtain the existence of solution (the lubricant pressure and the elastic rod displacement). More precisely, a sign restriction on fluid pressure for cavitation modelling and different unilateral conditions on the rod displacement associated with a rigid structure coating are formulated in terms of coupled variational inequalities. The particular hinged or clamped boundary conditions on the rod displacement require different techniques to prove the existence of solution. Besides nearly linear coupled problems, two nonlinear rod problems including curvature effects are analysed. Mainly, regularity results and \(L^{\infty}\) estimates for the solution of variational inequalities and fixed-point theorems lead to the existence results for the various coupled models.

MSC:
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74G25 Global existence of solutions for equilibrium problems in solid mechanics (MSC2010)
74G40 Regularity of solutions of equilibrium problems in solid mechanics
49J40 Variational inequalities
76D08 Lubrication theory
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References:
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