A study on wrinkling characteristics and dynamic mechanical behavior of membrane

An eigenvalue method considering the membrane vibration of wrinkling out-of-plane deformation is introduced, and the stress distributing rule in membrane wrinkled area is analyzed. A dynamic analytical model of rectangular shear wrinkled membrane and its numerical analysis approach are also developed. Results indicate that the stress in wrinkled area is not uniform, i.e. it is larger in wrinkling wave peaks along wrinkles and two ends of wrinkle in vertical direction. Vibration modes of wrinkled membrane are strongly correlated with the wrinkling configurations. The rigidity is larger due to the heavier stress in the part of wrinkling wave peaks. Therefore, wave peaks are always located at the node lines of vibration mode. The vibration frequency obviously increases with the vibration of wave peaks.     

Finite deformation and stability behaviour of spherical inflatables subjected to axi-symmetric hydrostatic loading

This paper deals with the large deflection and stability behaviour of inextensible spherical air-supported membranes subjected to an accumulating ponding fluid. It is assumed that ponding fluid is available to fill an initial axi-symmetric deformation around the apex and that due to such accumulation deflections increase until under certain conditions collapse of the structure occurs.The problem is reduced to a set of differential equations which are solved numerically to determine the parameters defining the deflected wrinkled shape of the membrane. A simple expression for use in design of such structures is obtained and the results presented in non-dimensional graphic form.     

Coupled free vibration analysis of a fluid-filled rectangular container with a sagged bottom membrane

In the present paper, two-dimensional coupled free vibrations of a fluid-filled rectangular container with a sagged bottom membrane are investigated. This system consists of two rigid walls and a membrane anchored along two rigid vertical walls. It is filled with incompressible and inviscid fluid. The membrane material is assumed to act like an inextensible material with no bending resistance. First, the nonlinear equilibrium equation is solved and the equilibrium shape of the membrane is obtained using an analytical formulation neglecting the membrane weight. The small vibrations about the equilibrium configuration are then investigated. Along the contact surface between the bottom membrane and the fluid, the compatibility requirement is applied for the fluid–structure interactions and the finite element method is used to calculate the natural frequencies and mode shapes of the fluid–membrane system. The vibration analysis of the coupled system is accomplished by using the displacement finite element for the membrane and the pressure fluid-finite element for the fluid domain. The variations of natural frequencies with the pressure head, the membrane length, the membrane weight and the distance between two rigid walls are examined. Moreover, the mode shapes of system are investigated.     

Mechanics of a thin,tensioned shell,wrapped helically around a turn-bar

The fluid–structure interactions between a flexible web and an externally pressurized air cushion are modeled allowing for the possibility of contact. The web is wrapped around a porous, cylindrical turn-bar at an oblique angle (helically). The turn-bar supplies pressurized air into the web/turn-bar clearance to float the web. The shell model, developed to represent the mechanics of the web, allows it to be wrapped around the cylinder in a helical fashion. The fluid mechanics of the air in the web/turn-bar clearance is a two-dimensional form of the incompressible Navier–Stokes equations averaged in the clearance direction and augmented by nonlinear source terms. Contact between the web and the reverser, which is undesirable in a turn-bar application, is included in the model in order to enable the analysis of the limiting cases. The coupled equilibrium between fluid mechanics, shell deflections and contact is found numerically. This paper describes the theory. Case studies are conducted in order to understand the mechanics of the coupled system, and to make design recommendations. It is shown that the helix angle has a strong influence on the equilibrium configurations: increasing helix-angle results in increased web-reverser separation, while the air pressure settles to a lower value. This behavior is due to the reduced shell stiffness and belt-wrap pressure for the helically wrapped webs. Conditions that render a nearly uniform web/turn-bar clearance in the circumferential direction are identified. The supply pressure and airflow rates necessary to prevent web-scratches are calculated.     

On the gating of mechanosensitive channels by fluid shear stress

Mechanosensation is an important process in biological fluid–structure interaction. To understand the biophysics underlying mechanosensation, it is essential to quantify the correlation between membrane deformation,membrane tension, external fluid shear stress, and conformation of mechanosensitive(MS) channels. Smoothed dissipative particle dynamics(SDPD) simulations of vesicle/cell in three types of flow configurations are conducted to calculate the tension in lipid membrane due to fluid shear stress from the surrounding viscous flow. In combination with a simple continuum model for an MS channel, SDPD simulation results suggest that shearing adhered vesicles/cells is more effective to induce membrane tension sufficient to stretch MS channels open than a free shear flow or a constrictive channel flow. In addition, we incorporate the bilayer–cytoskeletal interaction in a two-component model to probe the effects of a cytoskeletal network on the gating of MS channels.     

Large deformation adhesive contact mechanics of circular membranes with a flat rigid substrate

We study the large deformation mechanics of contact and adhesion between an inflated hyperelastic membrane and a rigid substrate. The initial configuration of the membrane is flat and circular and is clamped at the edge. Two types of friction conditions between the membrane and the substrate are considered: frictionless and no-slip contact. We derive an exact expression for the energy release rate in terms of local variables at the contact edge, thus linking adhesion to the contact angle. Our model can account for the effects of fluid pressure for experiments performed in solution. We also extend our formulation to include surface tension. Numerical simulations for a neo-Hookean membrane are carried out to study the relation between applied pressure and contact area.     

Experiment and evaluation of wrinkling strain in a corner tensioned square membrane

Prediction of wrinkling characteristics is strongly correlated with the strain perpendicular to wrinkling direc- tion. In this paper, the strain field of wrinkled membrane is tested by VIC-3D system based on the digital image correlation technique. Experimental results are validated by the tension wrinkling simulation. The experimental strain perpendicular to wrinkling direction is analyzed in depth. The wrinkling strain of a square wrinkled membrane under corner tension is extracted from experimental strain perpendicular to wrinkling direction. A quantitative characterization format of the experimental wrinkling strain is proposed. A modified prediction method of wrinkling amplitude is presented based on the experimental wrinkling strain. The re- sults show that the precision of modified prediction model has improved 13.2% compared with the classical prediction model. The results reveal that the modified model can give an accurate prediction of the wrinkling amplitude.     

Analysis of pulled axisymmetric membranes with wrinkling

The nonlinear behavior of an axisymmetric hyperelastic membrane subjected to pulling forces is analyzed. The membrane is considered to be ideal in the sense that it cannot carry compressive stress resultants. If the membrane has a positive initial Gaussian curvature, the pulling gives rise to wrinkles which form over parts of the surface. The full nonlinear equations governing the membrane behavior in the doubly tense and in the wrinkled regions are formulated, and then solved using a numerical integration procedure. Solutions for various examples are presented, with Hookean and neo-Hookean constitutive behavior. These include a few examples of wrinkled membranes with positive initial Gaussian curvatures, and one example of a membrane with a negative initial Gaussian curvature, where no wrinkles are formed.     

Simulation of a pulsatile total artificial heart: Development of a partitioned Fluid Structure Interaction model

Heart disease is one of the leading causes of death in the world. Due to a shortage in donor organs artificial hearts can be a bridge to transplantation or even serve as a destination therapy for patients with terminal heart insufficiency. A pusher plate driven pulsatile membrane pump, the Total Artificial Heart (TAH) ReinHeart, is currently under development at the Institute of Applied Medical Engineering of RWTH Aachen University.This paper presents the methodology of a fully coupled three-dimensional time-dependent Fluid Structure Interaction (FSI) simulation of the TAH using a commercial partitioned block-Gauss–Seidel coupling package. Partitioned coupling of the incompressible fluid with the slender flexible membrane as well as a high fluid/structure density ratio of about unity led inherently to a deterioration of the stability (‘artificial added mass instability’). The objective was to conduct a stable simulation with high accuracy of the pumping process. In order to achieve stability, a combined resistance and pressure outlet boundary condition as well as the interface artificial compressibility method was applied. An analysis of the contact algorithm and turbulence condition is presented. Independence tests are performed for the structural and the fluid mesh, the time step size and the number of pulse cycles. Because of the large deformation of the fluid domain, a variable mesh stiffness depending on certain mesh properties was specified for the fluid elements. Adaptive remeshing was avoided. Different approaches for the mesh stiffness function are compared with respect to convergence, preservation of mesh topology and mesh quality. The resulting mesh aspect ratios, mesh expansion factors and mesh orthogonalities are evaluated in detail. The membrane motion and flow distribution of the coupled simulations are compared with a top-view recording and stereo Particle Image Velocimetry (PIV) measurements, respectively, of the actual pump.     

Free vibration of membrane/bounded incompressible fluid

Vibration of a circular membrane in contact with a fluid has extensive applications in industry.The natural vibration frequencies for the asymmetric free vibration of a circular membrane in contact with a bounded incompressible fluid are derived in this paper.Considering small oscillations induced by the membrane vibration in an incompressible and inviscid fluid,the velocity potential function is used to describe the fluid field.Two approaches are used to derive the free vibration frequencies of the system,which include a variational formulation and an approximate solution employing the Rayleigh quotient method.A good correlation is found between free vibration frequencies evaluated by these methods.Finally,the effects of the fluid depth,the mass density,and the radial tension on the free vibration frequencies of the coupled system are investigated.     

双层金属纳米板界面能密度的尺寸效应

界面能密度是表征纳米复合材料与结构界面力学性质的重要物理量.采用分子动力学方法计算了不同面心立方金属晶体构成的双材料纳米薄板结构的界面能密度,分析了界面晶格结构形貌变化及界面效应对原子势能的影响.结果表明:双材料纳米薄板界面具有周期性褶皱状疏密相间的晶格结构形貌,界面上原子势能亦呈现周期性分布特性,而靠近界面的两侧原子势能与板内原子势能具有明显差异.拉格朗日界面能密度和欧拉界面能密度均随双层薄板厚度的增加而增加,最终趋向于块体双材料结构的界面能密度.     

Boundary slippage for generating hydrodynamic load-carrying capacity

Boundary slippage is used to generate the load-carrying capacity of the hydrodynamic contact between two parallel plane surfaces. In the fluid inlet zone, the fluidcontact interfacial shear strength on a stationary surface is set at low to generate boundary slippage there, while in the fluid outlet zone the fluid-contact interfacial shear strength on the stationary surface is set at high enough to prevent the occurrence of boundary slippage. The fluid-contact interfacial shear strength on the entire moving surface is set at high enough to prevent boundary slippage on the moving surface. These hydrodynamic contact configurations are analyzed to generate the pronounced load-carrying capacity. The optimum ratio of the outlet zone width to the inlet zone width for the maximum load-carrying capacity of the whole contact is found to be 0.5.     

Fluid flow properties for different classes of intermediate wettability as studied by network modelling

Most clastic reservoirs display an intermediate type of wettability. Intermediate wettability covers several local wetting configurations like fractional wet and mixed-wet where the oil-wet sites could either be in the large or smaller pores. Clastic reservoirs show a large variation in fluid flow properties. A classical invasion–percolation network simulator is used to investigate properties of different intermediate wet situations. Variation in wetting properties like contact angles, process dependent contact angles, contact angle distribution, and fraction of oil wet sites are investigated. The fluid flow properties analysed in particular are residual oil saturation and normalized endpoint relative permeability. Results from network modelling have been compared to reservoir core analysis data. The network models applied are at the capillary limit, while the core flood results are clearly viscous influenced. Even though network modelling does not cover all the physics involved in fluid displacement processes, results show that data from simulations are sufficient to present trends in fluid flow properties which are comparable to experimental data.     

Fluid-structure interaction with an application to a body immersed and anchored in a fluid flow

In this paper, an implicit coupling algorithm for fluid–structure interaction problems with under-time steps for the solid is presented. Its implementation on two configurations is achieved by using the CASTEM finite-elements code. First, the free oscillations of a cylinder in an annular fluid domain where its movement is determined by the coupled fluid–solid action is considered in the case of viscous fluid. It should be noted that the implicit coupling algorithm gives the best prediction of the structure oscillations. The under-time steps for the solid are introduced in order to obtain better results. Then, an application whose final objective is to model a floating barrage is studied. The main goal of this application is to predict the displacements of a ring completely immersed and anchored by a cable to the lower boundary of the fluid domain. The finite-element discretization of the Navier–Stokes equations in the ALE formulation is used     

On the general contact problem of an inflated nonlinear plane membrane

The nonaxisymmetric contact problem between an inflated membrane and a rigid indentor is considered. The membrane is assumed to be an initially thin plane sheet. The shape and the boundary of the contact region and the configuration of the deformed membrane under both inflation and indentation are found by employing the minimum potential energy principle subjected to an inequality constraint condition. A slack variable that converts the inequality constraint to an equality constraint condition is introduced. The coordinate functions that describe the deformed configurations of the membrane are assumed to be represented by a series of geometric admissible functions with unknown coefficients. The unknown coefficients that minimize the total potential energy are determined by Fletcher and Powell's[1] iterative descent method for finding the minimum of a function of multivariables.     

Analysis of Constitutive Assumptions for the Strain Energy of a Generalized Elastic Membrane in a Nonlinear Contact Problem

For very thin shell-like structures it is common to ignore bending effects and model the structure using simple membrane theory. However, since the thickness of the membrane is not modeled explicitly in simple membrane theory it is not possible to use the three-dimensional strain energy function directly. Approximations must be introduced like the assumptions of: no thickness changes, generalized plane stress or incompressibility. In contrast, the theory of a Cosserat generalized membrane uses the three-dimensional strain energy function directly, it includes both thickness changes and shear deformation and it allows contact conditions to be formulated on the interface of the membrane with another body instead of on the middle surface of the membrane. A specific nonlinear contact problem is used to study these effects and comparison is made with solutions of a hierarchy of theories which include different levels of deformation through the thickness of the membrane and different formulations of the contact conditions. The results indicate that within the context of a simple membrane the assumption of generalized plane stress is best for this problem and that a generalized contact condition extends the range validity of the simple membrane solution to thicker membranes.     

Equilibrium of an Elastic Spherical Shell Filled with a Heavy Fluid under Pressure

This paper considers the problem of equilibrium of a nonlinearly elastic spherical shell filled with a heavy fluid and resting on a smooth, absolutely rigid, flat surface. The weight of the shell is assumed to be negligible in comparison with the weight of the fluid filling it. The contact region with the supporting plane is one of the unknowns in the problem. Equilibrium equations for a membrane shell are obtained in an accurate nonlinear formulation. Stresses and strains of a shell made of a Mooney–Rivlin material are numerically investigated. The results are compared with calculation results for the case of inflation of a spherical shell ignoring the weight of the fluid filling. The effect of the fluid weight on shell strains and stresses is estimated.     

Deflections and buckling of a bent elastica in contact with a flat surface

A straight elastica is bent until its ends are vertical and a fixed distance apart, and then it is pushed onto a flat rigid surface. The weight of the strip and friction between the strip and the surface are neglected. Planar equilibrium states of the strip are investigated, using either a shooting method or an integral formulation. Both symmetric and asymmetric configurations are possible. There may be a single point of contact, a flat region of contact, or two points of contact with a buckled section between them. Also, if the ends are pushed down sufficiently far, one or two loops may form when the upper portion of the strip makes contact with the lower portion on the surface. If the two ends are held together (vertically) and then pushed down, asymmetric configurations may occur in which there is a region of contact between the upper and lower portions of the strip near their ends. The properties of these various equilibrium shapes are investigated.     

Measurements of junction coupling during water hammer in piping systems

For the analysis of the effects of fluid–structure interaction (FSI) during water hammer in piping systems, a test facility has been designed and constructed. The research objective is to show on the basis of two specific examples that the necessity of considering FSI is strongly dependent on the boundary conditions of the system. Resonance experiments on movable bends in two piping system configurations focused on junction coupling were carried out. These configurations differ in the length of the hydraulic system and in the geometry of the oscillating bend. The displacement of the bend and the pressure inside the pipe were measured for various free oscillating lengths of the bend while the rest of the piping system was restrained. The results are displayed in resonance curves and frequency spectra for the different configurations. In both cases a correlation between the pressure and the displacement spectrum shows a transfer of momentum from the fluid to the structure, but only in the configuration with the long oscillating pipe section can a reaction of the fluid on the motion of the structure be identified. Frequency shifts of the pressure and a splitting of the pressure peak were observed. The time signals confirm that the effects of FSI are most significant in one system configuration which is strongly influenced by the bend geometry. Furthermore a parameter is presented which quantifies the effects of junction coupling based on the geometrical and hydraulic properties of the bend and the system.     

CFD-DEM simulation of the hole cleaning process in a deviated well drilling: The effects of particle shape

We investigate the effect of particle shape on the transportation mechanism in well-drilling using a three-dimensional model that couples computational fluid dynamics (CFD) with the discrete element method (DEM). This numerical method allows us to incorporate the fluid–particle interactions (drag force, contact force, Saffman lift force, Magnus lift force, buoyancy force) using momentum exchange and the non-Newtonian behavior of the fluid. The interactions of particle−particle, particle−wall, and particle−drill pipe are taken into account with the Hertz–Mindlin model. We compare the transport of spheres with non-spherical particles (non-smooth sphere, disc, and cubic) constructed via the multi-sphere method for a range of fluid inlet velocities and drill pipe inclination angles. The simulations are carried out for laboratory-scale drilling configurations. Our results demonstrate good agreement with published experimental data. We evaluate the fluid–particle flow patterns, the particle velocities, and the particle concentration profiles. The results reveal that particle sphericity plays a major role in the fluid–solid interaction. The traditional assumption of an ideal spherical particle may cause inaccurate results.