应用数学和力学

Evolution of a 2-D Disturbance in a Supersonic Boundary Layer and the Generation of Shocklets

HUANG Zhang-feng, ZHOU Heng

2004, 25(1): 1-8.

Abstract(3596) PDF(788)

Abstract:
Through direct numerical simulation,the evolution of a 2-D disturbance in a supersonic boundary layer has been investigated.At a chosen location,a small amplitude T-S wave was fed into the boundary layer to investigate its evolution.Characteristics of non-linear evolution have been found.Two methods were applied for the detection of shocklels,and it was found that when the amplitude of the disturbance reached a certain value,shocklets would be generated,which should be taken into consideration when non-linear theory of hydrodynamic stability for compressible flows is to be estabfished.

Quasi-Variational Principle for the Vortex-Potential Function of Rotational Flow in Three-Dimension Pipe

SHEN Yuan-sheng, LIU Gao-lian, LIU Yong-jie

2004, 25(1): 9-13.

Abstract(3023) PDF(669)

Abstract:
The variational analysis of the Pseudo-potential function-vortex-potential function model,a new mathematical model,was developed and by which the flow field with transonic speed and curl was decided,and different sorts of the variational principle for vortex potential function were established by transforming the original equation for vortex-function,the boundary conditions for vortex-potential function was raised.

New Numerical Method for Volterra Integral Equationof the Second Kind in Piezoelastic Dynamic Problems

DING Hao-jiang, WANG Hui-ming, CHEN Wei-qiu

2004, 25(1): 15-21.

Abstract(3009) PDF(600)

Abstract:
The elastodynamic problems of piezoelectric hollow cylinders and spheres under radial deformation can be transformed into a second kind Volterra integral equation about a function with respect to time,which greatly simplifies the solving procedure for such elastodynamic problems.Meanwhile,it becomes very important to find a way to solve the second kind Volterra integral equation effectively and quickly.By using an interpolation function to approadmate the unknown function,two new recursive formulae were derived,based on which numerical solution can be obtained step by step.The present method can provide accurate numerical results efficiently.It is also very stable for long time calculating.

Thereto-Piezoelectric Effects on the Postbuckling of Axially-Loaded Hybrid Laminated Cylindrical Panels

SHEN Hui-shen

2004, 25(1): 22-34.

Abstract(3029) PDF(591)

Abstract:
A compressive postbuclding analysis is presented for a laminated cylinderical panel with piezoelectric actuators subjected to the combined action of mechanical,electrical and thermal loads.The temperature field considered is assumed to be a uniform distribution over the panel surface and through the panel thickness and the electric field is assumed to be the transverse component E_Z only.The material properties are assumed to be independent of the temperature and the electric field.The governing equations are based on the classical shell theory with von Kármán-Donnell-type of ldnematic nonlinearity.The nonlinear prebuckling deformations and initial geometric imperfections of the panel are both taken into account.A boundary layer theory of shell buckling,which includes the effects of nonlinear prebuckling deformations,large deflections in the postbuckling range,and initial geometric imperfections of the shell,is extended to the case of hybrid laminated cylindrical panels of finite length.A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths.The numerical illustrations concern the compressive postbuckling behavior of perfect and imperfect,cross-ply laminated cylindrical thin panels with fully covered or embedded piezoelectric actuators under different sets of thermal and electrical loading conditions.The effects played by temperature rise,applied voltage,stacking sequence,the character of in-plane boundary conditions,as well as initial geometric imperfections are studied.

Stress Distribution Near Grain Boundary in Anisotropic Bicrystals and Tricrystals

WAN Jian-song, YUE Zhu-feng

2004, 25(1): 35-41.

Abstract(2446) PDF(571)

Abstract:
The rate dependent crystallographic finite element program was implemented in ABAQUS as a UMAT for the analysis of the stress distributions near grain boundary in anisotropic bicrystals and tricrystals,taking the different crystallographic orientations into consideration.The numerical results of bicrystaLs model with the different crystallographic orientations shows that there is a high stress gradient near the grain boundaries.The characteristics of stress structures are dependent on the crystallographic orientations of the two grains.The eadsting of triple Junctions in the tricrystals may result in the stress concentrations,or may not,depending on the crystallographic orientations of the three grains.The conclusion shows that grain boundary with different crystallographic orientations can have different deformation,damage,and failure behaviors.So It is only on the detail study of the stress distribution can the metal fracture be understood deeply.

Non-Interior Smoothing Algorithm for Frictional Contact Problems

ZHANG Hong-wu, HE Su-yan, LI Xing-si

2004, 25(1): 42-52.

Abstract(2826) PDF(691)

Abstract:
A new algorithm for solving the three-dimensional elastic contact problem with friction is presented.The algorithm is a non-interior smoothing algorithm based on an NCP-function.The parametric variaxional principle and parametric quadratic programming methods wwe applied to the analysis of three-dimensional frictional contact problem.The solution of the contact problem was finally reduced to a linear complementarily problem,which was reformulated as a system of nonsmooth equalions via an NCP-function.A smoothing approximation to the nonsmooth equations was given by the aggregate function.A Newton method was used to solve the resulting smoothing nonlinear equations.The algorithm presented is easy to understand and implement.The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.

Unsteady/Steady Numerical Simulation of Three-Dimensional Incompressible Navier-Stokes Equations on Artificial Compressibility

WEN Gong-bi, CHEN Zuo-bin

2004, 25(1): 53-66.

Abstract(4145) PDF(980)

Abstract:
A central and upwind difference scheme mixed algorithm are presented for soh}ing steady/unsteady three dimensional incompressible Navier-Stokes equations on artifical compressibility.The left side equations were implicit approximate factorizated and used centered difference scheme.The numerical flux on the right side of semi-discretized equations was calculated using the Roe approximate Riemann solver with three order accuracy.The algebraic turbulence model of Badwin-Lomax was used.Two dimensional flat,airfoil,prolate spheroid and cerebral aneurysm were calculated as examples compared with experiment data.The results show that the coefficient of pressure and skin friction computed consistent with experimental data,the largest discrepancy occur in the separation region where Badwin-Lomax algebraic turbulence model could not exactly predict the flow.

New Exact Solutions to KdV Equations With Variable Coefficients or Forcing

FU Zun-tao, LIU Shi-da, LIU Shi-kuo, ZHAO Qiang

2004, 25(1): 67-73.

Abstract(2864) PDF(686)

Abstract:
Jacobi elliptic function expansion method is extended to construct the exact solutions to another kind of KdV equations,which have variable coefficients or forcing terms.And new periodic solutions obtained by this method can be reduced to the soliton-typed solutions under the limited condition.

Mixed Finite Element Methods for the Shallow Water Equations Including Current and Silt Sedimentation (Ⅰ)-The Continuous-Time Case

LUO Zhen-dong, ZHU Jiang, ZENG Qing-cun, XIE Zheng-hui

2004, 25(1): 74-84.

Abstract(2749) PDF(592)

Abstract:
An initial-boundary value problem for shallow equation system consisting of water dynamics equations,silt transport equation,the equation of bottom topography change,and of some boundary and initial conditions is studied,the existence of its generalised solution and semidiscrete mixed fuute element(MFE) solution was discussed,and the error estimates of the semidiscrete MFE solution was derived.The error estimates are optimal.

Forebody Compressibility Research of Hypersonic Vehicle

LIU Jia, YAO Wen-xiu, LEI Mai-fang, WANG Fa-min

2004, 25(1): 85-92.

Abstract(2624) PDF(547)

Abstract:
Three kinds of forebody model of hypersonic vehicles were studied with numerical simulation method.It shows that the two-order compressive ramp model is the best selection among the three for its good evaluative parameters value at the cowl of the inlet.This model can provide higher value of flux coefficient and total pressure recovery coefficient and lower average Mach number compared with those of the other two models.Simultaneously different compressive angles may have different effects.The configuration which the first order of compressive angle is 4° and the second 5° is the optimum combination.Furthermore factors such as attack angle were concerned.Better result may be obtained with a range of attack angles.Based on the work above the integrated design for forebody/inlet of a hypersonic vehicle was performed.The numerical result shows that this integrated model provides good flow field quality for inlet and engine work.

Exact Solutions for Nonlinear Transient Flow Model Including a Quadratic Gradient Term

CAO Xu-long, TONG Deng-ke, WANG Rui-he

2004, 25(1): 93-99.

Abstract(2645) PDF(624)

Abstract:
The models of the nonlinear radial flow for the infinite and finite reservoirs including a quadratic gradient term were presented.The enact solution was given in real space for flow equation including quadratic gradiet term for both constant-rate and constant pressure production cases in an infinite system by using generalized Weber transform.Analytical solutions for flow equation including quadratic gradient term were also obtained by using the Hankel transform for a finite circular reservoir case.Both closed and constant pressure outer boundary conditions are considered.Moreover,both constant rate and constant pressure inner boundary conditions are considered.The difference between the nonlinear pressure solution and linear pressure solution is analyzed.The difference may be reached about 8% in the long time.The effect of the quadratic gradient term in the large time well test is considered.

J^* Integral of the Specific Deviator Strain Energy and Its Application

JIANG Yu-chuan, WANG Qi-zhi

2004, 25(1): 100-110.

Abstract(3014) PDF(542)

Abstract:
First the deviator strain energy is introduced,then the problem of plane-crack critical growth was discussed,a path independent line integral J^* was defined,furthermore its conservation was proved strictly.As application examples,mode-Ⅰ stress intensity factors of cracked beam were obtained with present approach.The results were shown to agree well with those available in the open literature.

2004 Vol. 25, No. 1