徐州矿区采空塌陷区公路工程地质灾害与防治对策分析

采用格子Boltzmann方法模拟可变形膜与周围流体的相互作用. 分析了格子Boltzmann 方法中的边界处理方法和边界受力的计算方法，并且用此方法计算流场中可变形膜的受力. 可将离散化后的膜看作一系列的质点，从而得到膜的动力学方程. 将可变形膜在流场中受到 的力引入方程中，可以计算膜的变形. 求解了几种不同情况下，膜的形状随时间的变化. 发现，如果可变形膜非常软或者非常硬，经过足够长的时间后，膜的形状会接近一 条直线，即回到初始状态. 模拟过程是二阶精度的.     

Deformation of a tensile membrane adjacent to a moving wall caused by viscous flow

Theoretical analysis is done for deformation of a tensile membrane caused by viscous flow between the membrane and a solid boundary (wafer) placed adjacent to the membrane. The membrane and its support are assumed to have circular shapes. The boundary is assumed to move perpendicularly to the membrane by a small fraction of the gap width. The Hele–Shaw flow theory is applied to the flow. Variation of the central gap width is obtained, and it is shown that the maximum membrane deformation depends on the membrane tension and the final gap width. The dependence agrees with experimental results.     

Mechanical model of round window membrane under reverse excitation

According to the vibration characteristics of the round window, a mechanical model of a round window membrane is established. The Euler equation of the round window and the complementary boundary conditions are derived by the variational principle. Combined with the Bessel function, an analytical solution of the round window displacement is obtained by MATHEMATICA. Combined with clinical characteristics of round window membrane lesion, the effect of sound transmission due to thickening of the round window membrane caused by the otitis media, shrinkage of the round window membrane area caused by otosclerosis, and hardening of the round window membrane itself is analyzed. The results show that with thickening of the round window membrane, the displacement of the round window membrane is decreased. In the meantime, with hardening of the round window membrane and shrinkage of the membrane area, the maximum displacement of the round window membrane is gradually reduced, leading to a decrease in sound transmission. Thus, the analytical analysis can avoid interference of environment and the technical level of personnel, and it can evaluate transmission performance of the round window membrane efficiently, providing a theoretical basis for the reverse excitation of artificial prosthesis.     

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.     

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建立了薄膜褶皱分析的力学模型,并基于张力场理论和稳定性理论分析了褶皱区域的应 力应变关系. 在此基础上提出了褶皱薄膜动态分析的NBA-UM(nonlinear buckling analysis-update matrix)分析方法，分析了褶皱薄膜振动特性. 结 果表明，褶皱使薄膜产生``过度收缩' 现象，并改变了薄膜中的应力分布. 褶皱对薄膜的振动特性有很大的影响，大幅度的褶皱改 变了薄膜振动的固有频率和模态形式. 提出的NBA-UM分析方法可以有效地预报褶皱薄膜 的动态行为.     

PVDF涂层建筑膜材单元结构力学性能的试验研究

使用PVDF涂层建筑膜材制成的结构,在承受外载荷情况下,力学行为非常复杂。在本文中,重点研究其单元结构在承受外载荷情况下的力学性能。首先,对PVDF涂层建筑膜材进行拉伸试验,测定其在常温和低温环境下膜的拉伸力学性能参数。然后,以制成的三角框架结构膜单元为对象,在常温条件下,从有限元分析和实际加载试验两方面计算得出结构单元在均布载荷下的位移、应变和应力分布。最后,对其进行强度验证,得出采用膜单元构建大型建筑是安全的结论。试验方法和结果可以应用于膜建筑结构的设计。     

Cylindrical membrane partially stretched on a rigid cylinder

We consider the equilibrium problem of a hyperelastic thin-walled tube. One end of the tube is placed over an immovable, rough, rigid cylinder. We assume that the deformation of the tube is finite and axisymmetric. The tube is modeled by a cylindrical membrane. The membrane is composed of an incompressible, homogeneous, isotropic elastic material. We use Bartenev–Khazanovich (Varga) strain energy function. A contact between the membrane and the rigid cylinder is with a dry friction. The membrane will not slide off the cylinder only by a friction and at a sufficient contact area. The friction is described by Coulomb's law. We study a minimum length of the membrane which is in contact with the rigid cylinder and is needed to the equilibrium of the membrane.     

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.     

空间薄膜结构褶皱的数值模拟最新研究进展

褶皱问题是高精度空间薄膜结构最关心的问题之一, 它是影响薄膜结构形面精度的关键因素. 由于薄膜结构褶皱机理的复杂性, 该问题一直没能得到很好的解决, 人们对褶皱的认识, 目前主要是通过试验观察和数值模拟等方法. 本文综述了空间薄膜结构褶皱数值研究的发展和现状, 并对其中重要的和被广泛采纳的方法进行了重点介绍和评述. 最后对褶皱数值分析方法所面临的问题及其发展趋势作了初步展望.      

轴对称环膜大变形的计算分析及其机械特性参数的回归研究

本文对轴对称膜大变形的一种理论模型进行了具体分析。给出了这种数学模型用于解决轴对称环膜的具体计算步骤，并介绍了此种计算程序在进行环膜机械特性参数回归时的计算分析。最后作了环膜拉伸实验，实验结果和理论计算吻合较好。     

Nonlinear vibrations and instabilities of a stretched hyperelastic annular membrane

The mathematical modeling for the nonlinear vibration analysis of a pre-stretched hyperelastic annular membrane under finite deformations is presented. The membrane is initially fixed along the inner boundary and then subjected to a uniform radial traction along its outer circumference and fixed along the outer boundary. The pre-stretched membrane in then subjected to a transversal harmonic pressure. The membrane material is assumed to be homogeneous, isotropic, and neo-Hookean. First, the solution of the radially stretched membrane is obtained analytically and numerically by the shooting method. The equations of motion of the stretched membrane are then obtained. By analytically and numerically solving the linearized equations of motion, the vibration modes and frequencies of the hyperelastic membrane are obtained, and these normal modes are used, together with the Galerkin method, to obtain reduced order models for the nonlinear dynamic analysis. A parametric analysis of the nonlinear frequency-amplitude relations, resonance curves, bifurcation diagrams and basins of attraction show the influence of the initial stretching ratio and membrane geometry on the type and degree of nonlinearity of the hyperelastic membrane under large amplitude vibrations. To check the accuracy of the reduced order models and the influence of the simplifying hypotheses on the results, the same problem is also analyzed using the finite element method. Excellent agreement is observed.     

Constitutive analysis of thin biological membranes with application to radial stretching of a hollow circular membrane

The constitutive analysis of the mechanical response of thin elastic membranes under inplane deformation is presented by using the multiplicative decomposition of the deformation gradient into its areal and distortional parts. Specific results are obtained for the Evans-Skalak form of the strain energy function. The solution to the problem of radial stretching of a hollow circular membrane obeying this constitutive model is then derived. The stress concentration factor is determined as a function of the relative hole size and the magnitude of the applied tension. The tension boundary is identified above which no compressive stress appears in the membrane. The limit boundary is introduced below which the membrane cannot support the applied loading without unstable wrinkling. For the loading between the tension and the limit boundary, nonuniformly distributed infinitesimal wrinkles appear within the inner portion of the membrane, carrying radial tension but no circumferential stress (tension field). The specific form of the strain energy function is used to describe this behavior, and to calculate the amount of the membrane area absorbed by infinitesimal wrinkles. The wrinkled portion is surrounded by the outer portion of the membrane carrying both radial and circumferential stresses. The limit boundary is reached when wrinkles spread throughout the membrane. It is shown that for a sufficiently large tension at the outer boundary, the wrinkling does not spread throughout the membrane no matter how large the applied tension at the inner boundary of the membrane is, provided that no rupture takes place. The limiting extent of the tension field in such cases is calculated. The linearized version of the analysis is characterized by a closed form solution.     

Fluid flow of incompressible viscous fluid through a non-linear elastic tube

The study of viscous flow in tubes with deformable walls is of specific interest in industry and biomedical technology and in understanding various phenomena in medicine and biology (atherosclerosis, artery replacement by a graft, etc) as well. The present work describes numerically the behavior of a viscous incompressible fluid through a tube with a non-linear elastic membrane insertion. The membrane insertion in the solid tube is composed by non-linear elastic material, following Fung’s (Biomechanics: mechanical properties of living tissue, 2nd edn. Springer, New York, 1993) type strain–energy density function. The fluid is described through a Navier–Stokes code coupled with a system of non linear equations, governing the interaction with the membrane deformation. The objective of this work is the study of the deformation of a non-linear elastic membrane insertion interacting with the fluid flow. The case of the linear elastic material of the membrane is also considered. These two cases are compared and the results are evaluated. The advantages of considering membrane nonlinear elastic material are well established. Finally, the case of an axisymmetric elastic tube with variable stiffness along the tube and membrane sections is studied, trying to substitute the solid tube with a membrane of high stiffness, exhibiting more realistic response.     

Solution for free vibration problem of membrane with unequal tension in two directions

In this paper, we obtain the analytic solution of free vibration frequency and mode shapes of rectangle, circle and elliptic membranes. The approximate solution of membrane with arbitrary boundary "is also obtained. All of these membranes are acted on by unequal tension in two directions.For the rectangle membrane, in this paper we transform its vibration equation into one of usual membranes by trnasforming the coordinate, thus it is easy to get the solution. For the circle membrane, first we transform the coordinate in the same way we deal with the rectangle membrane. Next we transform the vibration equation into the Mathieu equation, then we get a formula of frequency of that membrane with some Mathieu function’s property. In the solution the elliptic membrane is similar to that of the circle membrane.Finally, some examples are given.     

Free-molecular gas flow through an oscillating membrane

Free-molecular gas flow through a membrane oscillating in its own plane is investigated. The probability of the passage through the membrane by gas molecules is calculated as a function of dimensionless parameters characterizing the channel geometry, themolecularmass, the gas temperature, and the membrane oscillation frequency and amplitude. It is shown that the membrane permeability for one or another gas can be controlled by means of changing the forced oscillation parameters.     

On the non-linear vibrations of a circular membrane

Free axisymmetric vibrations of a stretched circular membrane are studied using a membrane theory consisting of a pair of non-linear partial differential equations coupled between the transverse and radial displacements of the membrane. A systematic perturbation method, in which the amplitude of the transverse displacement is taken as the perturbation parameter, is used to obtain periodic solutions of the non-linear equations. The initial membrane strain enters the problem as a parameter which is allowed to vary over a range of values. A case of self-resonance is encountered when the initial membrane strain approaches some critical values. This self-resonance case is also treated through an appropriate modification of the perturbation method.     

Tension of a cylindrical membrane partially stretched over a rigid cylinder

We study a contact problem with friction for a hyperelastic long thin-walled tube. One end of the tube is placed over an immovable, rough, rigid cylinder and an axial force is applied to another end. We assume the deformation of the tube is finite and axisymmetric. The tube is modeled by a semi-infinity cylindrical membrane. The axial force tends to a constant value at large distances from the inclusion. The membrane is made of an incompressible, homogeneous, isotropic elastic material. A contact between the membrane and the rigid cylinder is with a dry friction. The membrane will not slide off the cylinder only by friction and at a sufficient contact area. The friction is described by Coulomb’s law. We study a minimum length of the membrane which is in contact with the rigid cylinder and is needed to hold the membrane on the rigid cylinder. We obtain an explicit solution for the Bartenev–Khazanovich (Varga) strain–energy function and numerical results for the Mooney–Rivlin and Fung models.     

A theory of sound transmission through a clamped curved piezoelectric membrane connected to a negative capacitor

An analytical calculation of the acoustic transmission loss of sound propagating through a thin cylindrically curved piezoelectric membrane, which is rigidly clamped at its straight ends, is presented. The membrane is placed inside an acoustic tube and connected to an active electric shunt circuit that behaves as a negative capacitor. A properly adjusted shunt circuit has a significant impact on the effective elastic stiffness of the piezoelectric membrane and, hence, influences the membrane acoustic reflectivity and transmission loss of sound. Such a setup represents a noise control system based on the principles of the active elasticity control of piezoelectric materials. The non-uniform radial motion of the clamped membrane and its interaction with the acoustic field and the electric shunt circuit are analyzed. The main objective of the calculations, which are based on Donnell’s theory, is the determination of the effects of the membrane clamps on the flexural motion of the membrane and, therefore, effects on the acoustic transmission loss of sound. Approximative formulae for the amplitude of the membrane displacement and the acoustic transmission loss of sound are expressed as well as the resonant frequencies of the uniform mode and flexural vibration modes.     

膜材碰撞接触分析的向量式有限元法

向量式有限元是以向量力学理论为分析基础并基于点值描述来获得结构体系行为的新型分析方法。在简要介绍向量式有限元三角形膜单元基本理论的基础上,针对膜材与刚体、膜材与膜材两类碰撞接触问题,提出了碰撞检测和碰撞响应的处理方法。通过膜材质点与三角形网格面之间的单向碰撞检测方法来处理膜结构的碰撞检测问题;结合罚函数法和中央差分位移式,提出基于中央差分式的罚接触力响应方法,同时赋予罚参数的选取规则,以处理膜结构的碰撞响应问题。在此基础上编制了向量式有限元膜单元的碰撞接触分析程序,并通过算例分析验证了理论推导和编制程序的可靠性和计算稳定性,体现出向量式有限元方法进行膜材碰撞接触分析的优势。     

Electro-viscoelastic behaviors of circular dielectric elastomer membrane actuator containing concentric rigid inclusion

The time-dependent electro-viscoelastic performance of a circular dielectric elastomer (DE) membrane actuator containing an inclusion is investigated in the context of the nonlinear theory for viscoelastic dielectrics. The membrane, a key part of the actuator, is centrally attached to a rigid inclusion of the radius a, and then connected to a fixed rigid ring of the radius b. When subject to a pressure and a voltage, the membrane inflates into an out-of-plane shape and undergoes an inhomogeneous large deformation. The governing equations for the large deformation are derived by means of non-equilibrium thermodynamics, and viscoelasticity of the membrane is characterized by a rheological spring-dashpot model. In the simulation, effects of the pressure, the voltage, and design parameters on the electromechanical viscoelastic behaviors of the membrane are investigated. Evolutions of the considered variables and profiles of the deformed membrane are obtained numerically and illustrated graphically. The results show that electromechanical loadings and design parameters significantly influence the electro-viscoelastic behaviors of the membrane. The design parameters can be tailored to improve the performance of the membrane. The approach may provide guidelines in designing and optimizing such DE devices.