Finite element computations for unsteady fluid and elastic membrane interaction problems

The interaction between the hydrodynamic forces of a flow field and the elastic forces of adjacent deformable boundaries is described by elastohydrodynamics, a coupled fluid–elastic membrane problem. Direct numerical solution of the unsteady, highly non-linear equations requires that the dynamic evolution of both the flow field and the domain shape be determined as part of the solution, since neither is known a priori. This paper describes a numerical algorithm based on the deformable spatial domain space–time (DSD/ST) finite element method for the unsteady motion of an incompressible, viscous fluid with elastic membrane interaction. The unsteady Navier–Stoke and elastic membrane equations are solved separately using an iterative procedure by the GMRES technique with an incomplete lower-upper (ILU) decomposition at every time instant. One-dimensional, two-dimensional and deformable domain model problems are used to demonstrate the capabilities and accuracy of the present algorithm. Both steady state and transient problems are studied. © 1997 John Wiley & Sons, Ltd.     

The effect of texture on the shaft surface on the sealing performance of radial lip seals

On the basis of elastohydrodynamic model,the present study numerically analyzes the effect of various microdimple texture shapes,namely,circular,square,oriented isosceles triangular,on the pumping rate and the friction torque of radial lip seals,and determines the microdimple texture shape that can produce positive pumping rate.The area ratio,depth and shape dimension of a single texture are the most important geometric parameters which influence the tribological performance.According to the selected texture shape,parameter analysis is conducted to determine the optimal combination for the above three parameters.Simultaneously,the simulated performances of radial lip seal with texture on the shaft surface are compared with those of the conventional lip seal without any texture on the shaft surface.     

Elastohydrodynamics of tensioned web roll coating process

Coating process is an important step in the manufacturing of different products, such as paper, adhesive and magnetic tapes, photographic films, and many other. The tensioned web roll coating is one the several methods used by different industries. It relies on the elastohydrodynamic action between the fluid and the tensioned substrate for transferring and applying the liquid. The main advantage of this method is its ability to apply very thin liquid layers with less sensitivity to mechanical tolerance at relative small cost. Despite its industrial application, theoretical analysis and fundamental understanding of the process are limited. This work analyses this elastohydrodynamic action by solving the differential equations that govern the liquid flow, described by the Navier–Stokes equation, and the web deformation, modelled by the cylindrical shell approximation. The goal is to determine the operating conditions at which the process is two dimensional and defect free. The equations are discretized by the Galerkin/finite‐element method. The resulting non‐linear system of equations is solved by Newton's method coupled with pseudo‐arc‐length continuation in order to obtain solutions around turning points. The theoretical results are used to construct an operating window of the process that is in agreement with limited experimental data. Copyright © 2003 John Wiley & Sons, Ltd.     

Elastohydrodynamic problems in quasicrystal elasticity theory and wave propagation

Elastohydrodynamic problems of decagonal quasicrystals are analysed where the phonon field obeys wave equation and the phason field obeys diffusive wave equation. Basic equations are solved in the quasiperiodic plane and periodic plane, respectively. Final governing equations of dynamic behaviours of decagonal quasicrystals are obtained. A general solution is derived in terms of introduced three auxiliary functions, where two individually satisfy a fourth-order partial differential equation and one satisfies a second-order hyperbolic diffusion equation. Using the derived governing equations, elastic waves propagating in the quasiperiodic plane and a plane containing the period axis are analysed. Secular equations are obtained. It is found that differing from conventional crystals, at least four branches of elastic waves exist when the phonon–phason coupling is present. Moreover, acoustic waves have attenuation during wave propagation. Phason fluctuations exhibit exponential decaying behaviour due to kinematic viscosity and damping. The phase speeds are isotropic in the quasiperiodic plane and anisotropic in a plane with the periodic axis. The section of the slowness surfaces is plotted.