应用数学和力学

2004 Vol. 25, No. 7

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Optimal Control of Hyperbolic H-Hemivariational Inequalities With State Constraints

LU Wei-gang, GUO Xing-ming, ZHOU Shi-xing

2004, 25(7): 661-666.

Abstract(2241) PDF(631)

Abstract:
The optimal control problems of hyperbolic H-hemivariational inequalities with the state constraints and nonnomotone multivalued mapping term are considered.The optimal solutions are obtained.In addition,their approximating problems are also studied.

Investigation of the Behavior of a Griffith Crack at the Interface Between Two Dissimilar Orthotropic Elastic Half-Planes for the Opening Crack Mode

ZHOU Zhen-gong, WANG Biao

2004, 25(7): 667-676.

Abstract(3276) PDF(571)

Abstract:
The behaviors of an interface crack between dissimilar orthotropic elastic half-planes subjected to uniform tension was reworked by use of the Schmidt method.By use of the Fourier transform,the problem can be solved with the help of two pairs of dual integral equations,of which the unknown variables are the jumps of the displacements across the crack surfaces.Numerical examples are provided for the stress intensity factors of the cracks.Contrary to the previous solution of the interface crack,it is found that the stress singularity of the present interface crack solution is of the same nature as that for the ordinary crack in homogeneous materials.When the materials from the two half planes are the same,an exact solution can be otained.

Research on the Motion of Particles in the Turbulent Pipe Flow of Fiber Suspensions

ZHANG Wei-feng, LIN Jian-zhong

2004, 25(7): 677-685.

Abstract(2381) PDF(736)

Abstract:
The motion of fibers in turbulent pipe flow was simulated by 3-D integral method based on the slender body theory and simplified model of turbulence.The orientation distribution of fibers in the computational area for different Re numbers was computed.The results which were consistent with the experimental ones show that the fluctuation velocity of turbulence cause fibers to orient randomly.The orientation distributions become broader as the Re numer increases.Then the fluctuation velocity and angular velocity of fibers were obtained.Both are affected by the fluctuation velocity of turbulence. The fluctuation velocity intensity of fiber is stronger at longitudinal than at lateral,while it was opposite for the fluctuation angular velocity intensity of fibers.Finally,the spatial distribution of fiber was give.It is obvious that the fiber dispersion is strenghened with the increase of Re numbers.

Simulation Seismic Wave Propagation in Topographic Structures Using Asymmetric Staggered Grids

SUN Wei-tao, YANG Hui-zhu

2004, 25(7): 686-694.

Abstract(2672) PDF(534)

Abstract:
A new 3D finite-difference(FD)method of spatially asymmetric staggered grids was presented to simulate elastic wave pro pagation in to pographic structures.The method approximated the first-order elastic wave equations by irregular grids finite difference operator with second-order time precise and fourth-order spatial precise.Additional intro duced finite difference formula solved the asymmetric problem arisen in non-uniform staggered grid scheme.The method had nointer polation between the fine and coarse grids.All grids were computed at the same spatial iteration.Complicated geometrical structures like rough submarine inter face,fault and nonplanar inter faces were treated with fine irregular grids.Theor etical analysis and numerical simulations show that this method saves consider able memory and computing time,at the same time,has satisfactory stability and accuracy.

Distribution of Active Earth Pressure of Retaining Wall With Wall Movement of Rotation About Top

WANG Yuan-zhan, TANG Zhao-ping, ZHENG Bin

2004, 25(7): 695-700.

Abstract(2465) PDF(603)

Abstract:
Based on the Coulomb's theory that the earth pressure against the back of a retaining wall is due to the thrust exerted by the sliding wedge of soil from the back of the wall to a plane which passes through the bottom edge of the wall and has an inclination equal to the angle of H,the theoretical answers to the unit earth pressure,the resultant earth pressure and the point of application of the resultant earth pressure on a retaining wall were obtained for the wall movement mode of rotation about top.The comparisons were made among the formula presented here,the formula for the wall movement mode of translation,the Coulomb's formula and some experimental observations.It is demonstrated that the magnitudes of the resultant earth pressures for the wall movement mode of rotation about top is equal to that determined by the formula for the wall movement mode of translation and the Coulomb's theory.But the distribution of the earth pressure and the points of application of the resultant earth pressures have significant difference.

Exact Analysis of Wave Propagation in An Infinite Rectangular Beam

SUN Wei-ming, YANG Guang-song, LI Dong-xu

2004, 25(7): 701-710.

Abstract(2765) PDF(731)

Abstract:
The Fourier series method was extended for the exact analysis of wave propagation in an infinite rectangular beam.Initially,by solving the three-dimensional elastodynamic equations a general analytic solution was derived for wave motion within the beam.And then for the beam with stress-free boundaries,the propagation characteristics of elastic waves were presented.This accurate wave propagation model lays a solid foundation of simultaneous control of coupled waves in the beam.

Analytical Solution of Restrained Torsional Stresses and Displacement for Rectangular-Section Box Bar With Honeycomb Core

ZHANG Ying-shi, ZHANG Xing

2004, 25(7): 711-717.

Abstract(2480) PDF(505)

Abstract:
Differential equation of restrained torsion for rectangular-section box bar with honeycomb core was established and solved by using the method of undetermined function.Non-dimension normal stress,shear stress acting in the faceplate and shear stress acting in the honeycomb-core and warping displacement were deduced.Numerical analysis shows the normal stress attenuates quickly along x-axis.Normal stress acting on the crosssection at a distance of 20h from the fixed end is only one percent of that acting on the fixed end.

Drift Motion of Free-Rotor Gyroscope With Radial Mass-Unbalance

LIU Yan-zhu, XUE Yun

2004, 25(7): 718-722.

Abstract(2816) PDF(710)

Abstract:
The motion of a rigid body about fixed point with small radial mass-unbalance in homogeneous gravitational field was discussed.The dynamical equations described by state variables of the body were established,and approximate analytical solutions for a spinning body with high speed were obtained by use of the average method.The influence of the radial mass-unbalance of the rotor to the precession character of a free-rotor gyroscope was analyzed.And a physical explanation of the drift phenomenon of the gyro was given.An applicable formula of gyro's constant drift in analytical form was obtained,which is perfectly coincident with the numerical calculation.

Eigen Theory of Viscoelastic Dynamics Based on theKelvin-Voigt Model

GUO Shao-hua

2004, 25(7): 723-728.

Abstract(4030) PDF(1006)

Abstract:
Using the eigen theory of solid mechanics,the eigen properties of anisotropic viscoelastic bodies with Kelvin-Voigt model were studied,and the generalized Stokes equation of anisotropic viscoelastic dynamics was obtained,which gives the three-dimensional pattern of viscoelastical waves. The laws of viscoelastical waves of different anisotropical bodies were discussed.Several new conclusiones are given.

Stokes Flow Due to Fundamental Singularities Before a Plane Boundary

N. Aktar, F. Rahman, S. K. Sen

2004, 25(7): 729-734.

Abstract(2268) PDF(693)

Abstract:
A representation for the velocity and pressure fields in three dimensional Stokes flow was presented in terms of a biharmonic function A and a harmonic function B.This representation was used to establish a general theorem for the calculation of Stokes flow due to fundamental singularities in a region bounded by a stationary no-slip plane boundary.Collins's theorem for axisymmetric Stokes flow before a rigid plane follows as a special case of the the orem.A few illustrative examples are given to show its usefulness.

On the Numerical Solution of Quasilinear Wave Equation With Strong Dissipative Term

Aytekin Gülle

2004, 25(7): 735-740.

Abstract(2765) PDF(614)

Abstract:
The numerical solution for a type of quasilinear wave equation is studied.The three-level difference scheme for quasi-linear waver equation with strong dissipative term is constructed and the convergence is proved.The error of the difference solution is estimated.The theoretical results are controlled on a numerical example.

Basic Equations of the Problem of the Nonlinear Unsymmetrical Bending for Orthotropic Rectangular Thin Plate With Variable Thickness

HUANG Jia-yin

2004, 25(7): 741-744.

Abstract(2868) PDF(540)

Abstract:
Under the case of ignoring the body forces and considering components caused by diversion of membrane in vertical direction(z direction),the constitutive equations of the problem of the non-linear unsymmetrical bending for orthotropic rectangular thin plate with variable thickness are given; then introducing the dimensionless variables and three small parameters,the dimensionaless governing equations of the deflection function and stress function are given.

Uniformly Valid Asymptotic Solutions of the Nonlinear Unsymmetrical Bending for Orthotropic Rectangular Thin Plate of Four Clamped Edges With Variable Thickness

HUANG Jia-yin

2004, 25(7): 745-754.

Abstract(2683) PDF(512)

Abstract:
By using "the method of modified two-variable","the method of mixing perturbation" and introducing four small parameters,the problem of the non-linear unsymmetrical bending for orthotropic rectangular thin plate with linear variable thickness is studied.And the uniformly valid asymptotic solution of N th-order for eqsilon 1 and M th-order for epsilon 2 of the deflection functions and stress function are obtained.

Dynamic Buckling of Stiffened Plates Under Fluid-Solid Impact Load

ZHANG Tao, LIU Tu-guang, XIONG You-lun, ZHANG Wei-heng

2004, 25(7): 755-762.

Abstract(2171) PDF(571)

Abstract:
A simple solution of the dynamic buckling of stiffened plates under fluid-solid impact loading is presented.Based on large deflection theory,a discretely stiffened plate model has been used.The tangential stresses of stiffeners and in-plane displacement are neglected.Applying the Hamilton's principle,the motion equations of stiffened plates are obtained.The deflection of the plate is taken as Fourier series,and using Galerkin method the discrete equations can be deduced,which can be solved easily by Runge-Kutta method.The dynamic buckling loads of the stiffened plates are obtained from B-R curves.

Initial Layer Phenomena for a Class of Singular Perturbed Nonlinear System with Slow Variables

HUANG Wei-zhang, CHEN YU-sen

2004, 25(7): 763-770.

Abstract(2565) PDF(521)

Abstract:
The initial layer phenomena for a class of singular perturbe d nonlinear system with slow variables are studied.By introducing stretchy variables with different quantity levels and constructing the correction term of initial layer with different "thickness",the N-order approximate expansion of perturbed solution concerning small parameter is obtained,and the "multiple layer" phenomena of perturbed solutins are revealed.Using the fixed point theorem,the existence of perturbed solution is proved,and the uniformly valid asymptotic expansion of the solutions is given as well.