Study on fluid-structure interaction in liquid oxygen feeding pipe systems using finite volume method

The fluid-structure interaction may occur in space launch vehicles,which would lead to bad performance of vehicles,damage equipments on vehicles,or even affect astronauts’ health.In this paper,analysis on dynamic behavior of liquid oxygen (LOX) feeding pipe system in a large scale launch vehicle is performed,with the effect of fluid-structure interaction (FSI) taken into consideration.The pipe system is simplified as a planar FSI model with Poisson coupling and junction coupling.Numerical tests on pipes between the tank and the pump are solved by the finite volume method.Results show that restrictions weaken the interaction between axial and lateral vibrations.The reasonable results regarding frequencies and modes indicate that the FSI affects substantially the dynamic analysis,and thus highlight the usefulness of the proposed model.This study would provide a reference to the pipe test,as well as facilitate further studies on oscillation suppression.     

Interaction of subway LIM vehicle with ballasted track in polygonal wheel wear development

This paper develops a coupled dynamics model for a linear induction motor (LIM) vehicle and a subway track to investigate the influence of polygonal wheels of the vehicle on the dynamic behavior of the system. In the model, the vehicle is modeled as a multi-body system with 35 degrees of freedom. A Timoshenko beam is used to model the rails which are discretely supported by sleepers. The sleepers are modeled as rigid bodies with their vertical, lateral, and rolling motions being considered. In order to simulate the vehicle running along the track, a moving sleeper support model is introduced to simulate the excitation by the discrete sleeper supporters, in which the sleepers are assumed to move backward at a constant speed that is the same as the train speed. The Hertzian contact theory and the Shen- Hedrick-Elkins’ model are utilized to deal with the normal dynamic forces and the tangential forces between wheels and rails, respectively. In order to better characterize the linear metro system (LMS), Euler beam theory based on modal superposition method is used to model LIM and RP. The vertical electric magnetic force and the lateral restoring force between the LIM and RP are also taken into consideration. The former has gap-varying nonlinear characteristics, whilst the latter is considered as a constant restoring force of 1 kN. The numerical analysis considers the effect of the excitation due to polygonal wheels on the dynamic behavior of the system at different wear stages, in which the used data regarding the polygonal wear on the wheel tread are directly measured at the subway site.     

A spherical cavity expansion model for penetration of ogival-nosed projectiles into concrete targets with shear-dilatancy

A dynamic spherical cavity-expansion penetration model is suggested herein to predict the penetration and perforation of concrete targets struck normally by ogivalnosed projectiles.Shear dilatancy as well as compressibility of the material in comminuted region are considered in the paper by introducing a dilatant-kinematic relation.A procedure is first presented to compute the radial stress at the cavity surface and then a numerical method is used to calculate the results of penetration and perforation with friction being taken into account.The influences of various target parameters such as shear strength,bulk modulus,density,Poisson’s ratio and tensile strength on the depth of penetration are delineated.It is shown that the model predictions are in good agreement with available experimental data.It is also shown that the shear strength plays a dominant role in the target resistance to penetration.     

Indentation of a compressible soft electroactive half-space: Some theoretical aspects

We theoretically study the indentation response of a compressible soft electroactive material by a rigid punch. The half-space material is assumed to be initially subjected to a finite deformation and an electric biasing field. By adopting the linearized theory for incremental fields, which is established on the basis of a general nonlinear theory for electroelasticity, the appropriate equations governing the perturbed infinitesimal elastic and electric fields are derived particularly when the material is subjected to a uniform equibiaxial stretch and a uniform electric displacement. A general solution to the governing equations is presented, which is concisely expressed in terms of four quasi-harmonic functions. By adopting the potential theory method, exact contact solutions for three common perfectly conducting rigid indenters of flat-ended circular, conical and spherical geometries can be derived, and some explicit relations that are of practical importance are outlined.     

On the energy conservation and critical velocities for the propagation of a ＂steady-shock＂ wave in a bar made of cellular material

The propagation of shock waves in a cellular bar is systematically studied in the framework of continuum solids by adopting two idealized material models, viz. the dynamic rigid, perfectly plastic, locking （D-R-PP-L） model and the dynamic rigid, linear hardening plastic, locking （D-R-LHP-L） model, both considering the effects of strain-rate on the material properties. The shock wave speed relevant to these two models is derived. Consider the case of a bar made of one of such material with initial length L 0 and initial velocity v i impinging onto a rigid target. The variations of the stress, strain, particle velocity, specific internal energy across the shock wave and the cease distance of shock wave are all determined analytically. In particular the ＂energy conservation condition＂ and the ＂kinematic existence condition＂ as proposed by Tan et al. （2005） is re-examined, showing that the ＂energy conservation condition＂ and the consequent ＂critical velocity＂, i.e. the shock can only be generated and sustained in R-PP-L bars when the impact velocity is above this critical velocity, is incorrect. Instead, with elastic deformation, strain-hardening and strain-rate sensitivity of the cellular materials being considered, it is appropriate to redefine a first and a second critical impact velocity for the existence and propagation of shock waves in cellular solids. Starting from the basic relations for shock wave propagating in D-R-LHP-L cellular materials, a new method for inversely determining the dynamic stress-strain curve for cellular materials is proposed. By using e.g. a combination of Taylor bar and Hopkinson pressure bar impact experimental technique, the dynamic stress-strain curve of aluminum foam could bedetermined. Finally, it is demonstrated that this new formulation of shock theory in this one-dimensional stress state can be generalized to shocks in a one-dimensional strain state, i.e. for the case of plate impact on cellular materials, by simply making proper replacements of the elastic and plastic constants.     

Modeling finite thickness slab perforation using a coupled Eulerian–Lagrangian approach

A coupled Eulerian–Lagrangian (CEL) method can be used to model many types of dynamic events. Projectile penetration through solids is particularly well-suited to a CEL method. In this study the CEL method in the commercially-available code Abaqus was used to model a near rigid projectile perforating finite thickness concrete slabs. A near rigid projectile can be modeled as a Lagrangian material with distinct material interfaces, while the solid target can be modeled as an Eulerian material capable of large deformations. An improved concrete constitutive model is also described that was implemented into Abaqus as a user material model. A simplified stochastic model was also implemented to capture some of the heterogeneous nature of concrete. The CEL simulations are compared to experimental data to demonstrate the utility of this method for this type of perforation event.     

Attitude maneuver of liquid-filled spacecraft with a flexible appendage by momentum wheel

Attitude maneuver of liquid-filled spacecraft with an appendage as a cantilever beam by momentum wheel is studied.The dynamic equations are derived by conservation of angular momentum and force equilibrium principle.A feedback control strategy of the momentum wheel is applied for the attitude maneuver.The residual nutation of the spacecraft in maneuver process changes with some chosen parameters,such as steady state time,locations of the liquid container and the appendage,and appendage parameters.The results indicate that locations in the second and fourth quadrants of the body-fixed coordinate system and the second quadrant of the wall of the main body are better choices for placing the liquid containers and the appendage than other locations if they can be placed randomly.Higher density and thicker cross section are better for lowering the residual nutation if they can be changed.Light appendage can be modeled as a rigid body,which results in a larger residual nutation than a flexible model though.The residual nutation decreases with increasing absolute value of the initial sloshing angular height.     

Research of air-cushion isolation effects on high arch dam reservoir

A three-dimensional (3D) finite element model of air-cushion isolated arch dam is presented with the nonlinear gas-liquid-solid multi-field dynamic coupling effect taken into account.In this model,the displacement formulation in Lagrange method,pressure formulation in Euler method,nonlinear contact model based on Coulomb friction law are applied to the air-cushion,reservoir and contraction joint domain,respectively.The dynamic response of Jinping I arch dam with a height of 305 m is analyzed using the seismic records of the Wenchuan Earthquake in 2008.Numerical results show that the air-cushion isolation reduces significantly the hydrodynamic pressure as well as the opening width for the contraction joints of high arch dam.     

Deformation of plastically compressible hardening-softening-hardening solids

Motivated by a model of the response of vertically aligned carbon nanotube (VACNT) pillars in uniaxial compression, we consider the deformation of a class of compressible elastic-viscoplastic solids with a hardening-softening-hardening variation of flow strength with plastic strain. In previous work (Hutchens et al. 2011) a constitutive relation was presented and used to model the response of VACNT pillars in axisymmetric compression. Subsequently, it was found that due to a programming error the constitutive relation presented in the paper (Hutchens et al. 2011) was not the one actually implemented. In particular, the plastic flow rule actually used did not satisfy plastic normality. Here, we present the constitutive formulation actually implemented in the previous work (Hutchens et al. 2011). Dynamic, finite deformation, finite element calculations are carried out for uniaxial compression, uniaxial tension and for indentation of a "half-space" by a conical indenter tip. A sequential buckling-like deformation mode is found in com- pression when there is plastic non-normality and hardening-softening-hardening. The same material characterization gives rise to a Lüders band-like deformation mode in ten- sion. When there is a deformation mode with a sharp front along mesh boundaries, the overall stress-strain response contains high frequency oscillations that are a mesh artifact. The responses of non-softening solids are also analyzed and their overall stress-strain behavior and deformationmodes are compared with those of hardening-softening- hardening solids. We find that indentation with a sharp in- denter tip gives a qualitatively equivalent response for hardening and hardening-softening-hardening solids.     

A discrete model of a rope with bending stiffness or viscous damping

A discrete model of a rope is developed and used to simulate the plane motion of the rope fixed at one end.Actually,two systems are presented,whose members are rigid but non-ideal joints involve elasticity or dissipation.The dissipation is reflected simply by viscous damping model, whereas the bending stiffness conception is based on the classical curvature-bending moment relationship for beams and simple geometrical formulas.Equations of motion are derived and their complexity is discussed from the computational point of view.Since modified extended backward differentiation formulas(MEBDF)of Cash are implemented to solve the resulting initial value problems,the technique scheme is outlined.Numerical experiments are performed and influences of the elasticity and damping on behaviour of the model are analyzed.Basic energy principles are used to verify the obtained results.     

Analysis of axial strain in one-dimensional loading by different models

Different phenomenological equations based on plasticity, primary creep （as a viscoplastic mechanism）, secondary creep （as another viscoplastic mechanism） and different combinations of these equations are presented and used to describe the material inelastic deformation in uniaxial test. Agreement of the models with experimental results and with the theoretical concepts and physical realities is the criterion of choosing the most appropriate formulation for uniaxial test. A model is thus proposed in which plastic deformation, primary creep and secondary creep contribute to the inelastic deformation. However, it is believed that the hardening parameter is composed of plastic and primary creep parts. Accordingly, the axial plastic strain in a uniaxial test may no longer be considered as the hardening parameter. Therefore, a proportionality concept is proposed to calculate the plastic contribution of deformation.     

Precracking and interfacial delamination in a bi-material structure: Static and dynamic loadings

The behavior of a precracked bi-material structure interface under given static and dynamic axial loading is an interest object in the present paper.Firstly,it is shown that the shear-lag model is a proper tool to analyze a delamination process in a precracked bi-material structure undergoing static loading.Secondly,the"shear-lag model"is applied to the structure under dynamic loading.To solve the problem for an interface delamination of the structure and to determine the debond length along the interface,our own 2D boundary element method(BEM)code is proposed in the case of static loading,and the shear-lag model together with the Laplace transforms and half-analytical calculations are used in the case of dynamic loading.The interface layer is assumed as a very thin plate compared with the other two.The parametric(geometric and elastic)analysis of the debond length and interface shear stress is done. The results from the 2D BEM code proved the validity of analytical solutions to the shear-lag model.In the dynamic case,the influence of loading characteristics,i.e.,frequencies and amplitude fluctuations on the shear stress and the value of debond length for an interval of time,is discussed. The analysis of the obtained results is illustrated by an example of the modern ceramic-metal composite,namely cermet, and depicted in figures.     

THE DYNAMIC BEHAVIORS OF VISCOELASTIC PIPE CONVEYING FLUID WITH THE KELVIN MODEL

Based on the differential constitutive relationship of linear viscoelastic, material, a solid-liquid coupling vibration equation for viscoelastic pipe conveying fluid is derived by the D'Alembert's principle. The critical flow velocities and natural frequencies of the cantilever pipe conveying fluid with the Kelvin model (flutter instability) are calculated with the modified finite difference method in the form of the recurrence formula. The curves between the complex frequencies of the first, second and third mode and flow velocity of the pipe are plotted. On the basis of the numerical, calculation results, the dynamic behaviors and stability of the pipe are discussed. It should be pointed out that the delay time of viscoelastic material with the Kelvin model has a remarkable effect on the dynamic characteristics and stability behaviors of the cantilevered pipe conveying fluid, which is a gyroscopic non-conservative system.     

The axisymmetric long-wave interfacial stability of core-annular flow of power-law fluid with surfactant

The long wave stability of core-annular flow of power-law fluids with an axial pressure gradient is investigated at low Reynolds number. The interface between the two fluids is populated with an insoluble surfactant. The analytic solution for the growth rate of perturbation is obtained with long wave approximation. We are mainly concerned with the effects of shear-thinning/thickening property and interfacial surfactant on the flow stability. The results show that the influence of shear-thinning/thickening property accounts to the change of the capillary number. For a clean interface, the shear-thinning property enhances the capillary instability when the interface is close to the pipe wall. The converse is true when the interface is close to the pipe centerline. For shear-thickening fluids, the situation is reversed. When the interface is close to the pipe centerline, the capillary instability can be restrained due to the influence of surfactant. A parameter set can be found under which the flow is linearly stable.     

Effect of imperfect bonding on the dynamic response of a pre-stressed sandwich plate-strip with elastic layers and a piezoelectric core

In this paper,we consider the dynamic response of a pre-stressed sandwich plate-strip with a piezoelectric core and elastic layers under the action of a time-harmonic force resting on a rigid foundation.The investigation is carried out within the framework of the piecewise homogeneous body model by utilizing the exact equations of motion and relations of the linear theory of electro-elasticity.It is assumed that there is a shear-spring-type imperfect contact between the layers,but a complete contact between the plate-strip and the rigid foundation.A mathematical model of the problem is constructed,and the governing equations of motion are solved by employing the finite element method(FEM).Numerical results illustrating the influence of a change in the value of the shear-spring parameter on the dynamic response of the plate-strip are then presented.     

Test analysis of detection of damage to a complicated spatial model structure

A two-stage damage detection approach is proposed and experimentally demonstrated on a complicated spatial model structure with a limited number of measurements. In the experiment,five known damage patterns,including 3 brace damage cases and 2 joint damage cases,were simulated by removing braces and weakening beam-column connections in the structure. The limited acceleration response data generated by hammer impact were used for system identification,and modal parameters were extracted by using the eigensystem realization algorithm. In the first stage,the possible damaged locations are determined by using the damage index and the characteristics of the analytical model itself,and the extent of damage for those substructures identified at stage I is estimated in the second stage by using a second-order eigen-sensitivity approximation method. The main contribution of this paper is to test the two-stage method by using the real dynamic data of a complicated spatial model structure with limited sensors. The analysis results indicate that the two-stage approach is ableto detect the location of both damage cases,only the severity of brace damage cases can be assessed,and the reasonable analytical model is critical for successful damage detection.     

Coupling dynamic analysis of a liquid-filled spherical container subject to arbitrary excitation

Using spherical coordinates, the coupling nonlin- ear dynamic system of a liquid-filled spherical tank, which can be excited discretionarily, is deduced by the H-O variational principle, and the viscous damping is introduced via the liquid dissipation function. The kinetic equations of the coupling system are deduced by the relationship between the velocity of liquid particles and the disturbed liquid surface equation. Normal differential equations are obtained through the Galerkin method. An equivalent mechanical model is developed for liquid sloshing in a spherical tank subject to arbitrary excitation. The fixed and slosh masses, as well as the spring and damping constants, are determined in such a way as to satisfy the principle of equivalence. Numerical simulations illustrate the theoretical results in this paper as well.     

人车路系统三维耦合振动分析及舒适度评价

基于将车身视作三维弹性梁、车轮为刚性体的全车模型,人体采用坐姿并联动力模型,路面简化成Kelvin地基上的板,通过轮胎的刚性滚子接触模型将车辆与路面耦合在一起,建立起考虑人车、车路耦合作用的用于评价车辆乘坐舒适度的三维人车路耦合系统振动模型,并推导出其运动平衡方程;通过Galerkin法对路面方程进行离散,采用New-mark积分法对耦合系统方程组进行求解,对人车路系统振动响应进行了分析;采用人体加权振动加速度均方根值对车辆乘坐舒适度进行评价,并对系统各参数对车辆乘坐舒适度的影响进行探讨.数值分析表明:传统模型下车辆乘坐舒适度指标与本文模型的指标相差最高可达到约30％;在分析车辆振动响应及乘坐舒适度时,不能忽视车辆与路面、人体与车辆相互作用,系统各参数对车辆乘坐舒适度都有一定程度的影响.     

Dynamic analysis on generalized linear elastic body subjected to large scale rigid rotations

The dynamic analysis of a generalized linear elastic body undergoing large rigid rotations is investigated. The generalized linear elastic body is described in kine- matics through translational and rotational deformations, and a modified constitutive relation for the rotational deformation is proposed between the couple stress and the curvature tensor. Thus, the balance equations of momentum and moment are used for the motion equations of the body. The floating frame of reference formulation is applied to the elastic body that conducts rotations about a fixed axis. The motion-deformation coupled model is developed in which three types of inertia forces along with their incre- ments are elucidated. The finite element governing equations for the dynamic analysis of the elastic body under large rotations are subsequently formulated with the aid of the constrained variational principle. A penalty parameter is introduced, and the rotational angles at element nodes are treated as independent variables to meet the requirement of C1 continuity. The elastic body is discretized through the isoparametric element with 8 nodes and 48 degrees-of-freedom. As an example with an application of the motion- deformation coupled model, the dynamic analysis on a rotating cantilever with two spatial layouts relative to the rotational axis is numerically implemented. Dynamic frequencies of the rotating cantilever are presented at prescribed constant spin velocities. The maximal rigid rotational velocity is extended for ensuring the applicability of the linear model. A complete set of dynamical response of the rotating cantilever in the case of spin-up maneuver is examined, it is shown that, under the ultimate rigid rotational velocities less than the maximal rigid rotational velocity, the stress strength may exceed the material strength tolerance even though the displacement and rotational angle responses are both convergent. The influence of the cantilever layouts on their responses and the multiple displacement trajectories observed in the floating frame is simultaneously investigated. The motion-deformation coupled model is surely expected to be applicable for a broad range of practical applications.