Application of the probabilistic fracture mechanics method of predicting the fatigue life of tubular joints

ＡＰＰＬＩＣＡＴＩＯＮＯＦＴＨＥＰＲＯＢＡＢＩＬＩＳＴＩＣＦＲＡＣＴＵＲＥＭＥＣＨＡＮＩＣＳＭＥＴＨＯＤＯＦＰＲＥＤＩＣＴＩＮＧＴＨＥＦＡＴＩＧＵＥＬＩＦＥＯＦＴＵＢＵＬＡＲＪＯＩＮＴＳＮｉｅＧｕｏ－ｈｕａ（聂国华）ＷｅｎｇＺｈｉ－ｙｕａｎ（翁智远）...     

The problems of nonlinear bending for orthotropic rectangular plate with four clamped edges

（黄家寅）（秦圣立）ＴＨＥＰＲＯＢＬＥＭＳＯＦＮＯＮＬＩＮＥＡＲＢＥＮＤＩＮＧＦＯＲＯＲＴＨＯＴＲＯＰＩＣＲＥＣＴＡＮＧＵＬＡＲＰＬＡＴＥＷＩＴＨＦＯＵＲＣＬＡＭＰＥＤＥＤＧＥＳ￥ＨｕａｎｇＪｉａｙｉｎ;ＱｉｎＳｈｅｎｇｌｉ（ＱｕｆｕＮｏｒｍａｌＵｎ...     

THE ANALYTICAL STUDY ON THE LASER INDUCED REVERSE－PLUGGING EFFECT BY USING THE CLASSICAL ELASTIC PLATE THEORY（II）──REVERSE－BULGE MOTION

ＴＨＥＡＮＡＬＹＴＩＣＡＬＳＴＵＤＹＯＮＴＨＥＬＡＳＥＲＩＮＤＵＣＥＤＲＥＶＥＲＳＥ－ＰＬＵＧＧＩＮＧＥＦＦＥＣＴＢＹＵＳＩＮＧＴＨＥＣＬＡＳＳＩＣＡＬＥＬＡＳＴＩＣＰＬＡＴＥＴＨＥＯＲＹ（ＩＩ）──ＲＥＶＥＲＳＥ－ＢＵＬＧＥＭＯＴＩＯＮ￥(周益春，...     

Numerical modeling of the initial stage of the generation of unsteady vortices from sharp corner in plane compressible flow

ＮＵＭＥＲＩＣＡＬＭＯＤＥＬＩＮＧＯＦＴＨＥＩＮＩＴＩＡＬＳＴＡＧＥＯＦＴＨＥＧＥＮＥＲＡＴＩＯＮＯＦＵＮＳＴＥＡＤＹＶＯＲＴＩＣＥＳＦＲＯＭＳＨＡＲＰＣＯＲＮＥＲＩＮＰＬＡＮＥＣＯＭＰＲＥＳＳＩＢＬＥＦＬＯＷＨｕａｎｇＤｕｎ（黄敦）（Ｄｅｐａｒｔ．...     

THE PROBLEMS OF THE NONLINEAR UNSYMMETRICAL BENDING FOR CYLINDRICALLY ORTHOTROPIC CIRCULA RPLATE（I）

ＴＨＥＰＲＯＢＬＥＭＳＯＦＴＨＥＮＯＮＬＩＮＥＡＲＵＮＳＹＭＭＥＴＲＩＣＡＬＢＥＮＤＩＮＧＦＯＲＣＹＬＩＮＤＲＩＣＡＬＬＹＯＲＴＨＯＴＲＯＰＩＣＣＩＲＣＵＬＡＲＰＬＡＴＥ（Ｉ）ＱｉｎＳｈｅｎｇ－Ｉｉ（秦圣立）ＨｕａｎｇＪｉａ－ｙｉｎ（黄家寅）（Ｑｕｆ...     

NUMERICAL SIMULATION OF FLOW OF HIGHLY VISCOELASTIC FLOW IN THREE－DIMENSIONAL VARYING THICK SLIT CHANNEL

（杨伯源）（李勇）ＮＵＭＥＲＩＣＡＬＳＩＭＵＬＡＴＩＯＮＯＦＦＬＯＷＯＦＨＩＧＨＬＹＶＩＳＣＯＥＬＡＳＴＩＣＦＬＯＷＩＮＴＨＲＥＥ－ＤＩＭＥＮＳＩＯＮＡＬＶＡＲＹＩＮＧＴＨＩＣＫＳＬＩＴＣＨＡＮＮＥＬ￥ＹａｎｇＢｏｙｕａｎ；ＬｉＹｏｎｇ（Ｄｅｐａｒｔ...     

A UNIFORMLY CONVERGENT DIFFERENCE SCHEME FOR THE SINGULAR PERTURBATION PROBLEM OF A HIGH ORDER ELLIPTIC DIFFERENTIAL EQUATION

ＡＵＮＩＦＯＲＭＬＹＣＯＮＶＥＲＧＥＮＴＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＦＯＲＴＨＥＳＩＮＧＵＬＡＲＰＥＲＴＵＲＢＡＴＩＯＮＰＲＯＢＬＥＭＯＦＡＨＩＧＨＯＲＤＥＲＥＬＬＩＰＴＩＣＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮ（刘国庆）（苏煜城）ＡＵＮＩＦＯ...     

THE PROBLEMS OF THE NONLINEAR UNSYMMETRICAL BENDING FOR CYLINDRICALLY ORTHOTROPIC CIRCULAR PLATE（II）

ＴＨＥＰＲＯＢＬＥＭＳＯＦＴＨＥＮＯＮＬＩＮＥＡＲＵＮＳＹＭＭＥＴＲＩＣＡＬ．ＢＥＮＤＩＮＧＦＯＲＣＹＬＩＮＤＲＩＣＡＬＬＹＯＲＴＨＯＴＲＯＰＩＣＣＩＲＣＵＬＡＲＰＬＡＴＥ（ＩＩ）ＨｕａｎｇＪｉａｙｉｎ（黄家寅）;ＱｉｎＳｈｅｎｇｌｉ（秦圣立）;Ｘｉ...     

Reciprocal theorem method for solving the problems of bending of thick rectangular plates

ＲＥＣＩＰＲＯＣＡＬＴＨＥＯＲＥＭＭＥＴＨＯＤＦＯＲＳＯＬＶＩＮＧＴＨＥＰＲＯＢＬＥＭＳＯＦＢＥＮＤＩＮＧＯＦＴＨＩＣＫＲＥＣＴＡＮＧＵＬＡＲＰＬＡＴＥＳＦｕＢａｏ－ｌｉａｎ（付宝连）Ｔａｎｗｅｎ－ｆｅｎｇ（谭文锋）（ＹａｎｓｈａｎＵｎｉｒｅｒｓｉｔ...     

Effect of magnetic fields on viscous liquid column with finite length in a vertical straight tube

ＥＦＦＥＣＴＯＦＭＡＧＮＥＴＩＣＦＩＥＬＤＳＯＮＶＩＳＣＯＵＳＬＩＱＵＩＤＣＯＬＵＭＮＷＩＴＨＦＩＮＩＴＥＬＥＮＧＴＨＩＮＡＶＥＲＴＩＣＡＬＳＴＲＡＩＧＨＴＴＵＢＥＷｅｎＧｏｎｇ－ｂｉ（温功碧）;ＳｕｎＫｅ－ｌｉ（孙克利）（ＤｅｐａｒｔｍｅｎｔｏｆＭ...     

Transport in ordered and disordered porous media II: Generalized volume averaging

In this paper we develop the averaged form of the Stokes equations in terms of weighting functions. The analysis clearly indicates at what point one must choose a media-specific weighting function in order to achieve spatially smoothed transport equations. The form of the weighting function that produces the cellular average is derived, and some important geometrical theorems are presented.Roman Letters A interfacial area of the- interface associated with the local closure problem, m² - A _e area of entrances and exits for the-phase contained within the averaging system, m² - A _p surface area of a particle, m² - d _p 6V _p/A_p, effective particle diameter, m - g gravity vector, m/s² - I unit tensor - K _m permeability tensor for the weighted average form of Darcy's law, m² - L general characteristic length for volume averaged quantities, m - L _p general characteristic length for volume averaged pressure, m - L characteristic length for the porosity, m - L _v characteristic length for the volume averaged velocity, m - l characteristic length (pore scale) for the-phase - l _i i=1, 2, 3 lattice vectors, m - (y) weighting function - m(–y) (y), convolution product weighting function - _v special weighting function associated with the traditional averaging volume - m _v special convolution product weighting function associated with the traditional averaging volume - m _g general convolution product weighting function - m _V unit cell convolution product weighting function - m _C special convolution product weighting function for ordered media which produces the cellular average - m _D special convolution product weighting function for disordered media - m _M master convolution product weighting function for ordered and disordered media - n unit normal vector pointing from the-phase toward the-phase - p pressure in the-phase, N/m² - p_m superficial weighted average pressure, N/m² - p _m intrinsic weighted average pressure, N/m² - p traditional intrinsic volume averaged pressure, N/m² - p p p _m , spatial deviation pressure, N/m² - r ₀ radius of a spherical averaging volume, m - r _m support of the convolution product weighting function, m - r position vector, m - r position vector locating points in the-phase, m - V averaging volume, m³ - V volume of the-phase contained in the averaging volume, m³ - V _cell volume of a unit cell, m³ - V velocity vector in the-phase, m/s - vm superficial weighted average velocity, m/s - v _m intrinsic weighted average velocity, m/s - V volume of the-phase contained in the averaging volume, m³ - V _p volume of a particle, m³ - v traditional superficial volume averaged velocity, m/s - v v p _m spatial deviation velocity, m/s - x position vector locating the centroid of the averaging volume or the convolution product weighting function, m - y position vector relative to the centroid, m - y position vector locating points in the-phase relative to the centroid, m Greek Letters indicator function for the-phase - Dirac distribution associated with the- interface - V /V, volume average porosity - _m m * . weighted average porosity - mass density of the-phase, kg/m³ - viscosity of the-phase, Ns/m² - V /V, volume fraction of the-phase     

Evaluation of the dynamic-mechanical properties of solids from a cooperative model for stress relaxation

For many solid materials the stress relaxation process obeys the universal relationF = – (d/d lnt)_max = (0.1 ± 0.01) ( ₀ — _i ), regardless of the structure of the material. Here denotes the stress,t the time, ₀ the initial stress of the experiment and _i the internal stress. A cooperative model accounting for the similarity in relaxation behaviour between different materials was developed earlier. Since this model has a spectral character, the concepts of linear viscoelasticity are used here to evaluate the corresponding prediction of the dynamic mechanical properties, i.e. the frequency dependence of the storageE () and lossE () moduli. Useful numerical approximations ofE () andE () are also evaluated. It is noted that the universal relation in stress relaxation had a counterpart in the frequency dependence ofE (). The theoretical prediction of the loss factor for high-density polyethylene is compared with experimental results. The agreement is good.     

Filament stretching equation in Lagrangian coordinates

The general integral of the very simple equation ^21/n/() was found to describe the cross sectional area of filaments of isothermal power law fluids while in transient stretching where is time and is the initial location of fluid molecules at time = 0 given as the distance from a reference point fixed in space. Any such stretching transient given as a solution of the above equation is physically realizable subject to the restrictions > 0 and/ < 0.     

Bifurcations of Poiseuille flow between parallel plates: Three-dimensional solutions with large spanwise wavelength

The spatial dynamics approach is applied to the analysis of bifurcations of the three-dimensional Poiseuille flow between parallel plates. In contrast to the classical studies, we impose time periodicity as well as spatial periodicity with period 2/ in the streamwise direction. However, we make no assumptions on the behavior in the spanwise direction, except the uniform closeness of the bifurcating solution to the basic flow. In an abstract setting it is shown how the dimension of the critical eigenspace of the spatial dynamics analysis can be uniquely determined from the classical linear stability problem. For the three-dimensional Poiseuille problem we are able to find all relevant coefficients from the analysis of the purely two-dimensional problem. Moreover, we are able to analyze precisely the influence of a spanwise pressure gradient and the associated spanwise mass flux. The study of the reduced problem shows that there are two different kinds of solutions (spirals and ribbons) which are 2p/ periodic in the spanwise direction, as in the Couette-Taylor problem, and both of them bifurcate in the same direction.     

On surface waves in generalized thermoelasticity

Knowles' representation theorem for harmonically time-dependent free surface waves on a homogeneous, isotropic elastic half-space is extended to include harmonically time-dependent free processes for thermoelastic surface waves in generalized thermoelasticity of Lord and Shulman and of Green and Lindsay.r , , r , , .This work was done when author was unemployed.     

On laminar flow through a uniformly porous pipe

Numerous investigations ([1] and [4–9]) have been made of laminar flow in a uniformly porous circular pipe with constant suction or injection applied at the wall. The object of this paper is to give a complete analysis of the numerical and theoretical solutions of this problem. It is shown that two solutions exist for all values of injection as well as the dual solutions for suction which had been noted by previous investigators. Analytical solutions are derived for large suction and injection; for large suction a viscous layer occurs at the wall while for large injection one solution has a viscous layer at the centre of the channel and the other has no viscous layer anywhere. Approximate analytic solutions are also given for small values of suction and injection.

Nomenclature

General r distance measured radially - z distance measured along axis of pipe - u velocity component in direction of z increasing - v velocity component in direction of r increasing - p pressure - density - coefficient of kinematic viscosity - a radius of pipe - V velocity of suction at the wall - r ²/a ² - R wall or suction Reynolds number, Va/ - f() similarity function defined in (6) - u ₀() eigensolution - U(0) a velocity at z=0 - K an arbitrary constant - B _K Bernoulli numbers Particular Section 5 perturbation parameter, –2/R - ² a constant, –K - x / - g(x) f()/ Section 6 perturbation parameter, –R/2 - ² a constant, –K - g() f() - g _c ()=g() near centre of pipe - * point where g()=0 Section 7 2/R - ² K - t (1–)/ - w(t, ) [1–f(t)]/ - ₀, ₁ constants - g() f()– ₀ - ₀/ - ₀ a constant - * point where f()=0     

Mean and turbulent velocity measurements of supersonic mixing layers

The behavior of supersonic mixing layers under three conditions has been examined by schlieren photography and laser Doppler velocimetry. In the schlieren photographs, some large-scale, repetitive patterns were observed within the mixing layer; however, these structures do not appear to dominate the mixing layer character under the present flow conditions. It was found that higher levels of secondary freestream turbulence did not increase the peak turbulence intensity observed within the mixing layer, but slightly increased the growth rate. Higher levels of freestream turbulence also reduced the axial distance required for development of the mean velocity. At higher convective Mach numbers, the mixing layer growth rate was found to be smaller than that of an incompressible mixing layer at the same velocity and freestream density ratio. The increase in convective Mach number also caused a decrease in the turbulence intensity ( _u/U).List of symbols a speed of sound - b total mixing layer thickness between U ₁ – 0.1 U and U ₂ + 0.1 U - f normalized third moment of u-velocity, f u³/(U)³ - g normalized triple product of u² , g u²/(U)³ - h normalized triple product of u ², h u ²/(U)³ - l _u axial distance for similarity in the mean velocity - l _u axial distance for similarity in the turbulence intensity - M Mach number - M _c convective Mach number (for ₁ = ₂), M _c (U ₁ – U ₂)/(a ₁ + a ₂) - P static pressure - r freestream velocity ratio, r U ₂/U ₁ - Re unit Reynolds number, Re U/ - s freestream density ratio, s ₂/₁ - T _t total temperature - u instantaneous streamwise velocity - u deviation of u-velocity, uu – U - U local mean streamwise velocity - U ₁ primary freestream velocity - U ₂ secondary freestream velocity - average of freestream velocities, (U ₁ + U ₂)/2 - U freestream velocity difference, U U ₁ – U ₂ - instantaneous transverse velocity - v deviation of -velocity, – V - V local mean transverse velocity - x streamwise coordinate - y transverse coordinate - y ₀ transverse location of the mixing layer centerline - ensemble average - ratio of specific heats - boundary layer thickness (y-location at 99.5% of free-stream velocity) - similarity coordinate, (y – y ₀)/b - compressible boundary layer momentum thickness - viscosity - density - standard deviation - dimensionless velocity, (U – U ₂)/U - 1 primary stream - 2 secondary stream A version of this paper was presented at the 11th Symposium on Turbulence, October 17–19, 1988, University of Missouri-Rolla     

Normal forms for random diffeomorphisms

Given a dynamical system (,, ,) and a random diffeomorphism (): ^{d d} with fixed point at x=0. The normal form problem is to construct a smooth near-identity nonlinear random coordinate transformation h() to make the random diffeomorphism ()=h()^–1() h() as simple as possible, preferably linear. The linearization D(, 0)=:A() generates a matrix cocycle for which the multiplicative ergodic theorem holds, providing us with stochastic analogues of eigenvalues (Lyapunov exponents) and eigenspaces. Now the development runs pretty much parallel to the deterministic one, the difference being that the appearance of turns all problems into infinite-dimensional ones. In particular, the range of the homological operator is in general not closed, making the conceptof-normal form necessary. The stochastic versions of resonance and averaging are developed. The case of simple Lyapunov spectrum is treated in detail.     

Robustness of Exponential Dichotomies in Infinite-Dimensional Dynamical Systems

In this paper we examine the issue of the robustness, or stability, of an exponential dichotomy, or an exponential trichotomy, in a dynamical system on an Banach space W. These two hyperbolic structures describe long-time dynamical properties of the associated time-varying linearized equation _t +A=B(t) , where the linear operator B(t) is the evaluation of a suitable Fréchet derivative along a given solution in the set K in W. Our main objective is to show, under reasonable conditions, that if B(t)=B(, t) depends continuously on a parameter and there is an exponential dichotomy, or exponential trichotomy, at a value ₀, then there is an exponential dichotomy, or exponential trichotomy, for all near ₀.We present several illustrations indicating the significance of this robustness property.     

Generation of vortices in a partially filled,rapidly rotating cylinder

We describe a system in which vortices are shed from a cylindrical free surface approximately centered in a rotating flow. Shedding is controlled by the parameter =2 g/ ² d, where g, , d denote gravity, rotation rate and the diameter of the free surface. We find vortex shedding for >0.162 and no vortex shedding for < 0.0847. The range depends on the aspect ratio L/d, where L is the column length, in a nonmonotonic fashion. These results are independent of viscosity and surface tension for small values of these parameters.Now at Martin Marietta, Orlando Aerospace, PO Box 5837, Mail Point 150, Orlando, FL 32855, USA