Blowup properties for a class of nonlinear degenerate diffusion equation with nonlocal source

A nonlinear degenerate parabolic equation with nonlocal source was considered. It was shown that under certain assumptions the solution of the equation blows up in finite time and the set of blowup points is the whole region. The integral method is used to investigate the blowup properties of the solution.     

二维CE/SE算法改进及其高阶精度格式

通过提出一种新的守恒元和解元划分方式对二维时-空守恒元解元算法(CE/SE)进行了改进,推导了改进CE/SE算法的一、二阶精度计算格式,并给出了更高阶精度计算格式的构造方法。利用得到的改进CE/SE格式对激波反射问题、后台阶扰流问题及隔墙坑道传播问题进行了数值模拟。数值结果表明,对CE/SE算法的改进是成功的。改进CE/SE算法有诸多优点,值得在数值模拟中推广使用。     

Small twist of a circular cylindrical tube exhibiting cylindrical aeolotropy of a nonorthogonal type

Summary At each point of an elastic cylindrical tube the aeolotropy is defined with respect to a triad of nonorthogonal curves. When the tube undergoes a small twist the effect of the nonorthogonality appears in the form of extra terms in the expression for the couple on the tube. Restrictions on the elastic properties of the material are obtained for zero warping of the cylinder sections, and a solution is given when warping is present.     

Effect of the magnetic field on the pulsatile flow through a rigid tube

I.IntroductionThefunctionofanaPbliedmagneticfield\onhumanbodieshasbeenknownandservedasakindofthemedicaltreatmentforalongtime.ThemagneticstoneusedasamedicineisrdeordedinShennongMaterlbMedica,'which.isthefirstChinesemedicinebookandwaswrittenin200A.D..ItwasalsorecordedtyancientGreecethatholdingmagneticstQnesinhandsandfeetcouldrelievethepainandspasml'l.However,beinglimitedbythelevelQfproductionandmedicaltreatmentsatthattime,themagnetictreatmentwasmainlyusedforlocallydephlogisticating,relievin…     

矩形截面管内电流变液的流动

基于伽辽金方法，导出了矩形截面直管内泊肃叶流动的一阶和二阶近似解．在此基础上，研究了电流变单链的变形问题，并得到了描述它形状的多项式函数．     

Assessment of effect of heat of internal friction on characteristics of structured flow of viscoplastic liquid in a round tube

A structured pressure flow of viscoplastic liquid in an infinite round tube is examined. Energy dissipation is given due consideration; it is assumed that the temperature dependences of the plastic viscosity and the ultimate shear stress are exponential. The solution obtained when the parameter characterizing the rate of production of heat of internal friction is assumed to be small indicates that energy dissipation has a sgnificant effect on the local flow characteristics and the hydraulic-resistance coefficient, for which an expression suitable for engineering calculations is given.     

A Pressurized Functionally Graded Hollow Cylinder with Arbitrarily Varying Material Properties

The elastic analysis of a pressurized functionally graded material (FGM) annulus or tube is made in this paper. Different from existing studies, this study deals with an axisymmetrical FGM hollow cylinder or disk with arbitrarily varying material properties. A simple and efficient approach is suggested, which reduces the associated problem to solving a Fredholm integral equation. The resulting equation is approximately solved by expanding the solution as series of Legendre polynomials. The stresses and displacements can be represented in terms of the solution to the equation. For radius-dependent Young’s modulus, numerical results of the distribution of the radial and circumferential stresses are presented graphically. Our results indicate that change in the gradient of the FGM tube does not produce a substantial variation of the radial stress, but strongly affects the distribution of the hoop stress. In particular, the hoop stress may reach its maximum at an internal position or at the outer surface when the tube is internally pressurized. The results obtained are helpful in designing FGM cylindrical vessels to prevent failure.      

The dynamic response of an incompressible non-linearly elastic membrane tube subjected to a dynamic extension

The dynamic response of an isotropic hyperelastic membrane tube, subjected to a dynamic extension at its one end, is studied. In the first part of the paper, an asymptotic expansion technique is used to derive a non-linear membrane theory for finite axially symmetric dynamic deformations of incompressible non-linearly elastic circular cylindrical tubes by starting from the three-dimensional elasticity theory. The equations governing dynamic axially symmetric deformations of the membrane tube are obtained for an arbitrary form of the strain-energy function. In the second part of the paper, finite amplitude wave propagation in an incompressible hyperelastic membrane tube is considered when one end is fixed and the other is subjected to a suddenly applied dynamic extension. A Godunov-type finite volume method is used to solve numerically the corresponding problem. Numerical results are given for the Mooney-Rivlin incompressible material. The question how the present numerical results are related to those obtained in the literature is discussed.     

Analyticity of the solution of a plane elastoplastic problem

Elastoplastic problems of the theory of ideal plasticity were studied numerically by the method of small parameter in the monographs [1–3], and strengthening elastoplastic problems were studied in the monograph [4], where a rather complete bibliography of studies in this direction is given. The conditions for the continuous dependence of the the stress-strain state characteristics on the boundary conditions and the material inhomogeneity are defined using the implicit function theorem in [5, 6]. In the present paper, in the framework of the perturbation method, we determine the stress state in a cylindrical tube with nearly circular boundaries under the action of pressure. Using the implicit function theorem, we examine the existence and uniqueness of the solution of the problem. We show that its solution can be obtained in the case of any analytic shape of the boundary and any number of material physical-mechanical characteristics depending on finitely many small parameters. The results can be generalized to more complicated models of media. The results obtained in this paper are compared with already known results.     

Thermal analysis of an infinite tube during quenching

 This paper deals with a numerical solution of the two-dimensional convection–diffusion equation in an infinite domain, arising out of quenching of an infinite tube. On the wetted side, upstream of the quench front, a constant heat transfer coefficient is assumed. The downstream of the quench front as well as the inside surface of the tube are assumed to be adiabatic. The solution gives the quench front temperature as a function of various model parameters such as Peclet number, Biot number and the radius ratio. The solution has been found to be in good agreement with the available analytical solutions and thus validates the numerical procedure suggested. Received on 10 July 2000     

Rarefied Poiseuille flow in elliptical and rectangular tubes

An isothermal steady rarefied gas flow in a long channel (tube) of elliptical or rectangular cross-section under the action of a given pressure gradient (Poiseuille flow) is studied on the basis of the Bhatnagar-Gross-Krook model. The solution is obtained using a conservative higher-order method. The velocity field in a channel cross-section is investigated as a function of the rarefaction degree and the cross-section geometry parameters. The main calculated function is the gas flow rate through the tube. The solutions obtained are compared with the available results.     

Blow-up of solution for a generalized Boussinesq equation

This paper studies the initial boundary value problem for a generalized Boussinesq equation and proves the existence and uniqueness of the local generalized solution of the problem by using the Galerkin method.Moreover,it gives the sufficient conditions of blow-up of the solution in finite time by using the concavity method.     

Extension,inflation and torsion of a residually stressed circular cylindrical tube

In this paper, we provide a new example of the solution of a finite deformation boundary-value problem for a residually stressed elastic body. Specifically, we analyse the problem of the combined extension, inflation and torsion of a circular cylindrical tube subject to radial and circumferential residual stresses and governed by a residual-stress dependent nonlinear elastic constitutive law. The problem is first of all formulated for a general elastic strain-energy function, and compact expressions in the form of integrals are obtained for the pressure, axial load and torsional moment required to maintain the given deformation. For two specific simple prototype strain-energy functions that include residual stress, the integrals are evaluated to give explicit closed-form expressions for the pressure, axial load and torsional moment. The dependence of these quantities on a measure of the radial strain is illustrated graphically for different values of the parameters (in dimensionless form) involved, in particular the tube thickness, the amount of torsion and the strength of the residual stress. The results for the two strain-energy functions are compared and also compared with results when there is no residual stress.     

用管轴流速确定动脉中血液振荡流的速度剖面

本文通过求解圆管内血液振荡流的基本方程，求得圆管内血液流的速度与压力梯度之间的关系式，文章提出一种利用管轴外流速计算管内压力梯度，进而确定血液振荡流动速度分布的方法，该方法用于检测活体血管内血液振荡流的速度剖面，具有操作简单，精度较高的优点，最后，以人体颈动脉为例，讨论血液周期振荡流的速度分布特征，发现在任意时刻，除了邻近管壁速度迅速降为零之外，沿管截面速度分布相当均匀，呈现出与定常流不同的速度分布特征。     

Large deflections of a beam subject to three-point bending

In this paper, a solution for the equilibrium configuration of an elastic beam subject to three-point bending is given in terms of Jacobi elliptical functions. General equations are derived, and the domain of the solution is established. Several examples that illustrate a use of the solution are discussed. The obtained numerical results are compared with the results of other authors. An approximation formula by which the beam load is given as a polynomial function of beam deflection is also derived. The range of applicability of the approximation is illustrated by numerical examples.     

Hydrodynamic theory of supercavitating pumps or hydroturbines

The article sets forth a three-dimensional linearized theory of a supercavitating pump or hydroturbine with finite dimensions of the blades and cavities, in a tube of round cross section. A fundamental solution is constructed (the potential of a source in a tube), and numerical methods are indicated for solution of the direct and inverse problems, required for the detailed design and calculation of axial hydromachines, under conditions of developed cavitation. Some results of the calculations are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 153–158, January–February, 1976.     

Closed-form expression of the similarity solutions for an air-filled, heavy membrane tube section on an incline

In this study, an air-filled, heavy membrane tube section resting on an incline is considered. The shape of the tube section is determined by the equilibrium of its weight and the transmural pressure. All quantities are normalized to obtain similarity solutions. A system of nonlinear ordinary differential equations with undetermined boundary conditions is solved analytically. The closed-form solutions are expressed in terms of the non-dimensional pressure for a given inclination angle. Using the results of this study, one can estimate the shape and characteristic values of a tube section without the burden of numerical calculations.