Self-similar cylindrical magnetogasdynamic and ionizing shock waves

Self-similar flows behind a cylindrical blast wave in magnetogasdynamics are studied. The shock is assumed to be propagating in a medium at rest with non-uniform density permeated by an azimuthal magnetic field generated by a constant line current passing along the line source of the blast wave. The shock is a magnetogasdynamic or ionizing type according as the electrical conductivity of the gas is infinite everywhere or infinite behind the shock and zero ahead of it. For both these cases adiabatic flows as well as flows with zero temperature gradient (Isothermal) are considered. Numerical solutions for the same are obtained and a comparative study is made. It is found that, for Isothermal flows, self similar solutions do not exist, when the ambient density varies as the inverse square of the distance from the axis of symmetry along which flows the line current. A particular analytical solution has been obtained for the adiabatic flow.     

The motion induced by the orthogonal stretching and shearing of a membrane beneath a quiescent fluid

The flow induced above an impermeable membrane undergoing orthogonal linear stretching and orthogonal linear shearing is investigated. For an exact solution of the Navier–Stokes equations, the orthogonal shearing motions must be related through the constant σ = γ δ, where γ and δ are the dimensionless streamwise and transverse shear rates, respectively. The resulting similarity reduction leads to three nonlinearly coupled ordinary differential equations governed by σ and the ratio of membrane stretch rates β. All possible solutions of these equations are found either numerically or, in special cases, analytically. Features of the σ = 0 solutions at β = 0 and asymptotically as β → ∞ are found to be in excellent agreement with numerical calculations. An aside calculation shows that orthogonal shearing in the absence of any plate stretching cannot exist. However, shearing in one coordinate direction is possible as long as the membrane stretches in at least one direction with the caveat that there exists uniform suction through a porous membrane.     

The Collapse Response of Sandwich Beams with Aluminium Face Sheets and a Metal Foam Core

Plastic collapse modes of simply supported and clamped sandwich beams have been investigated experimentally and theoretically, for aluminium face sheets and Alporas foam core. The effect of clamped boundary conditions is to induce axial stretching after the initial yield mechanism. Hence, face sheet ductility dictates the level of energy absorption of the beam. Numerical and analytical predictions are validated by the available experimental evidence.     

Multidomain analytical-numerical solution for a rotating magneticfield with a finite-length conducting cylinder

This paper treats the rotating magnetic field produced by a cylindrical sheet of temporally and azimuthally periodic axial electric current with a finite-length, electrically conducting cylinder surrounded by an electrical insulator inside the current sheet. As the frequency is increased, the magnetic field produced by the induced current in the cylinder cancels progressively more of the current-sheet magnetic field in the interior of the cylinder. This paper presents results for several different frequencies and for several different length-to-diameter ratios for the cylinder. It compares the results at the midplane of a long cylinder to the analytical solution for an infinitely long cylinder. It also compares results for a high frequency to the predictions from the first two terms in an asymptotic expansion for high frequency     

Superfluid films on a cylindrical surface

Superfluid films adsorbed on a cylindrical surface are studied. The superfluid density is calculated using a modification of the Kosterlitz-Thouless theory. There is no vortex unbinding transition because the vortex interaction is linear on long length scales. Thus the superfluid areal density, defined in terms of the real part of a response function, is nonzero for all T. The superfluid density is anisotropic, differing for axial and azimuthal flows. Dissipation due to vortex motion is considered. The periodicity of the substrate leads to a zero frequency dissipation mechanism for flows in the axial direction.     

具有非均匀热压强磁流体速度的定量研究

应用数值模拟方法,研究了非均匀等离子体压强梯度对圆柱位型磁流体速度的影响,并与均匀等离子体压强时的结论进行了比较,得到的主要结论包括:压力梯度对径向速度几乎无影响。无论等离子体压强是否均匀,角向速度和轴向速度的演化规律相似,但轴向速度对压力梯度更敏感。当等离子体压强均匀时,角向速度和轴向速度均为负值;当等离子体压强非均匀时,角向速度和轴向速度均正负参半,这体现了等离子体压强梯度对磁流体不稳定性的驱动效应。由于等离子壁对流体的阻碍作用,所有速度在等离子体壁处均衰减为零。     

Behavior and asymptotic stability of thermomechanical processes

Adiabatic shearing flows of incompressible Newtonian fluids with temperature-dependent viscosity under time-dependent inertial force and time periodic or steady boundary velocity are considered. We obtain some results concerning the behavior and the asymptotic stability of these flows for several types of shearing and viscosity functions.     

Meso-scaled progressive forming of bulk cylindrical and flanged parts using sheet metal

In microforming, handling and transporting of meso/micro-sized intermediate preforms are difficult due to the influence of adhesive force on preform surfaces. In this research, the fabrication of meso-scaled bulk cylindrical and flanged parts by directly using sheet metal is investigated. The cylinder is made with a single stroke by shearing, while the flanged part is formed progressively via multi-stage shearing and extrusion. In forming of the flanged part, an intermediate preform is fabricated with sheet metal and a pre-pierced hole for positioning. The final part is blanked out from the sheet metal in the last operation. In such a way, the transporting, positioning and ejecting of the flanged part are facilitated. Furthermore, the characteristics of the developed meso-scaled forming process are extensively investigated. The shearing and fractured surfaces on both the cylindrical and flanged parts are found. The surface grains of the blanked cylinder have undergone severe deformation and been hardened, which increases the flow stress of the blanked cylinder. In addition, the longer cylinder and flanged part are obtained with fine-grained material. This implies that a larger amount of material flow to the lateral side of the workpiece in the case of coarse-grained material.     

On some exact solutions of steady constantly-inclined plane MGD flow problems

Steady, plane, inviscid, compressible, electrically-conducting and constantly-inclined magnetogasdynamic flows are considered. Exact solutions for spiral flows with radial and circular magnetic lines, and radial flows with spiral magnetic lines are obtained.     

CFRP布加固木梁界面粘结应力的试验研究和理论分析

为了研究CFRP布加固木梁的界面粘结应力,对6根CFRP布加固的木梁进行了静力试验,得到了碳纤维布端部的应变分布。由相邻两测点的应变计算出了CFRP布与木材的平均界面粘结剪应力。忽略碳纤维布和木梁的剪切变形,推导了在任意荷载作用下两者之间的界面粘结剪应力和粘结正应力的计算公式,并根据边界条件给出了在两点对称集中荷载作用下公式中的系数,应用该公式计算了试验梁碳纤维布端部的界面粘结剪应力和正应力,结果表明粘结剪应力的计算值与试验值吻合较好,说明该公式是可行的。     

Thinning as a failure criterion during sheet metal forming

Thinning during forming is often considered a failure criterion in the metal forming industry. It is believed that a critical amount of thinning takes place in a sheet metal before failure. In this study, varying widths of low-carbon steel sheets were punch stretched under laboratory conditions. Thinning during punch stretching was measured at various locations along the steel sheets. These measurements demonstrated that thinning during forming is not constant, but that it is a function of the strain path followed by the sheet. Hence, thinning should not be used as a failure criterion during forming of sheet metals.     

轴压粘弹性圆柱壳在横向扰动下的混沌行为

基于大挠度薄壳的Donnell-Kármán理论和Kelvin–Voigt粘弹性本构关系,对轴压粘弹性圆柱壳在横向扰动下的混沌行为进行了研究。导出了关于挠度和应力函数的控制方程,借助Galerkin原理将粘弹性圆柱壳的控制方程转化为二阶三次非线性微分动力系统,用Melnikov函数给出了系统发生Smale马蹄型混沌的临界条件。数值计算分析了轴压载荷和粘性阻尼系数对混沌运动的影响。通过分岔图、位移时程曲线、相平面图和Poincaré映射描述了系统的运动行为。研究表明：当轴压载荷与圆柱壳的材料参数满足一定关系时,系统才有可能发生Smale马蹄型混沌;随着轴压载荷的增大,混沌运动区域逐渐减小;随着粘性系数与外阻尼系数比值的增大,混沌运动区域逐渐减小;轴压粘弹性圆柱壳在横向扰动下既会发生定常运动也会发生混沌运动     

A simplified approach for incorporating thickness stress in the analysis of sheet metal forming using shell elements

A simplified scheme for considering the thickness stress of shell elements induced by contact is presented which improves the accuracy of sheet metal forming analysis. The yield function formulated on the basis of plane stress conditions is modified to incorporate the effect of transverse normal stress induced by contact forces acting on shell elements and return mapping routine is used to update in‐plane stresses at each time step. The transverse normal stress distributions in the thickness direction are determined using the analytic solution of the cylindrical tube under the internal pressure. As numerical examples, uni‐axial compression, bi‐axial tension and bending tests are treated. The problem of cylindrical cup drawing is also calculated. Each result is compared with the results obtained by the analysis using ABAQUS continuum elements. Copyright © 2002 John Wiley & Sons, Ltd.     

Generalized Crane flow induced by continuous surfaces stretching with arbitrary velocities

The boundary-layer flow induced by a permeable sheet stretching with general polynomial velocity distribution is considered. This generalizes the work of Kumaran and Ramanaiah (Acta Mech. 116: 229–233, 1996) who were the first to observe that a Crane-type solution exists for wall motion composed of arbitrary linear and quadratic stretching terms, as long as an appropriate lateral transpiration is applied. We solve explicitly the problem to an arbitrarily high degree of the polynomial stretching. This motivates the second part of our study which provides explicit boundary-layer solutions for arbitrary wall stretching, with suitable transpiration. These solutions describe generalized Crane flows whose reciprocal (dimensionless) thicknesses always coincide with the negative of their (dimensionless) entrainment velocities. The associated heat transfer problem is solved explicitly for arbitrary stretching when an appropriate surface temperature distribution is prescribed.     

A numerical study of pulsatile blood flow in an eccentric catheterized artery using a fast algorithm

The pulsatile blood flow in an eccentric catheterized artery is studied numerically by making use of an extended version of the fast algorithm of Borges and Daripa [J. Comp. Phys., 2001]. The mathematical model involves the usual assumptions that the arterial segment is straight, the arterial wall is rigid and impermeable, blood is an incompressible Newtonian fluid, and the flow is fully developed. The flow rate (flux) is considered as a periodic function of time (prescribed). The axial pressure gradient and velocity distribution in the eccentric catheterized artery are obtained as solutions of the problem. Through the computed results on axial pressure gradient, the increases in mean pressure gradient and frictional resistance in the artery due to catheterization are estimated. These estimates can be used to correct the error involved in the measured pressure gradients using catheters.     

Linear stability of non-Newtonian annular liquid sheets

Summary This paper reports a linear stability analysis of a non-Newtonian annular liquid sheet that is surrounded by nonviscous fluids in relative axial motion to it. It is shown that for a stress free basic flow the dispersion relation giving the absolute and convective instability mechanisms can be immediately obtained from the dispersion relation for a Newtonian sheet by introducing a wavenumber dependent viscosity. The stability behavior of the sheet is investigated numerically by a continuation algorithm, by which the solution branches of the dispersion relation, relevant for the stability information, can be traced. The results give a stability picture which covers the whole range of annular sheets from the cylindrical jet to the plane liquid curtain.     

Magnetohydrodynamic stagnation-point flow towards a stretching sheet

Steady two-dimensional stagnation-point flow of an incompressible viscous electrically conducting fluid over a flat deformable sheet is investigated when the sheet is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. It is shown that the velocity at a point decreases/increases with increase in the magnetic field when the free stream velocity is less/greater than the stretching velocity. Temperature distribution in the flow is obtained when the surface is held at a constant temperature.     

Stroh formalism based boundary integral equations for 2D magnetoelectroelasticity

This paper presents a novel approach for obtaining boundary integral equations of 2D anisotropic magnetoelectroelasticity. This approach is based on the holomorphy theorems and the Stroh formalism and allows developing of the integral equations for the aperiodic, singly and doubly periodic problems of magnetoelectroelasticity. Obtained equations contain the unknown discontinuities of displacement, electric and magnetic potentials and also traction, electric displacement and magnetic induction that allow adopting the existing boundary element procedures for their solution. Analytical solutions for systems of collinear permeable or impermeable cracks are obtained. Numerical boundary element solutions are obtained for the singly and doubly periodic sets of permeable and impermeable cracks in the magnetoelectroelastic medium and a half-plane. Comparison with analytical solutions and other available results validate the present formulations and numerical computation.     

On approximate solutions for the deformation of plane anisotropic beams

Plane deformation of anisotropic beams with narrow rectangular cross sections exhibits coupling of stretching, bending and transverse shearing. For anisotropic cantilever beams with a stiff end-cap under end forces and an end couple, assessments were made for approximate solutions by comparing these with numerically exact finite element (FE) solutions. Specific attention is given to point-wise or approximate satisfaction of the end-fixity conditions. As approximate methodologies, (i) the elementary polynomial form of Airy's stress function for the plane stress problem in a rectangular region, (ii) a Timoshenko-type beam theory, and (iii) the Bernoulli-Euler beam theory were selected. Among these, only the polynomial form of Airy's stress function violates the point-wise end-fixity conditions. Both the polynomial Airy stress function and the Timoshenko-type beam theory successfully model the effects of transverse shear deformation and the coupling of stretching and transverse deflection. Analytical solutions demonstrate that the normal shear coupling effect increases linearly with the thickness-to-span ratios in axial normal stress and axial displacement, while the coupling manifests quadratically in transverse displacement. The comparison of end displacements with the numerically exact FE solutions indicates that the polynomial form of Airy's stress function is no better than the Timoshenko-type beam theory. Similar conclusions were reached for the problem of uniformly loaded cantilever beams. It has been found that the accurate prediction of the deformation of thick anisotropic beams with significant normal-shear coupling requires the use of higher order theories.     

Electrohydrodynamic flow between parallel dielectric channels

Steady, accelerated, and pulsating electro-dynamic flows in a plane dielectric channel are considered, along with Couette flow. It is shown that for these types of electrohydrodynamic flows the effect is concentrated in a thin layer near the walls, which can considerably change the friction stress on the walls. Some exact solutions of the energy equation are obtained.