应用数学和力学

2008 Vol. 29, No. 12

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A New Method for Computing Laminar-Tubulent Trasition and Turbulence in Compressible Boundary Layers—PSE+DNS

DONG Ming, ZHANG Yong-ming, ZHOU Heng

2008, 29(12): 1387-1394.

Abstract(3206) PDF(658)

Abstract:
A new method for computing the laminar-turbulent transition and turbulence in compressible boundary layers was proposed.It is especially useful for the computation of laminar-turbulent transition and turbulence starting from small-amplitude disturbances.The laminar stage,up to the beginning of the breakdown in laminar-turbulent transition,was computed by parabolized stability equations(PSE).Then the direct numerical simulations(DNS) method was employed to compute the transition process and turbulent flow,for which the inflow condition was provided by using the disturbances obtained by PSE method up to that stage.In the two test cases,including a subsonic and a supersonic boundary layer,the transition locations and the turbulent flow obtained by this method agree well with those obtained by using only DNS method for the whole process.The merit of using our method is that the computational cost is much smaller than that using only DNS method.

Solution of the Two Dimensional Scattering Problem in Piezoelectric/Piezomagnetic Media by Polarization Method

HU Yang-fan, WANG Biao

2008, 29(12): 1395-1410.

Abstract(2904) PDF(641)

Abstract:
Using the polarization method,the scattering problem for a two dimensional inclusion embedded in infinite piezoelectric/piezomagnetic matrices is investigated.To achieve the purpose,the polarization method for two-dimensional piezoelectric/piezomagnetic "comparison body" was formulated for the first time.For simple harmonic motion,the kernel of the polarization method reduces to the 2-D time-harmonic Green's function, which is deduced using the Radon transform.The formalism was further simplified under certain conditions(low frequency of the incident wave and small diameter of the inclusion),where some explicit analytical expressions were obtained.The analytical solutions for generalized piezoelectric/piezomagnetic anisotropic composites were given first,followed by simplified results for piezoelectric composites.Based on the latter results,two numerical results were provided for an elliptical cylindrical inclusion in a PZT-5H-matrices,illustrating the effect of different factors(including size effect,shape effect,effect of the material properties,and piezoelectric effect) on the scattering cross-section.

Limit Analysis of Viscoplastic Thick-Walled Cylinder and Spherical Shell Under Internal Pressure Using a Strain Gradient Plasticity Theory

LI Mao-lin, FU Ming-fu

2008, 29(12): 1411-1416.

Abstract(2782) PDF(668)

Abstract:
Plastic limit load of viscoplastic thick-walled cylinder and spherical shell subjected to internal pressure is investigated analytically using a strain gradient plasticity theory.As a result,the current solutions can capture the size effect at the micron scale.Numerical results show that the smaller the inner radius of the cylinder or spherical shell,the more significant the scale effects.Results also show that the size effect is more evident with the increase of strain or strain-rate sensitivity index.The classical plastically-based solutions of the same problems are shown to be a special case of the present solution.

Synchronization Motions of a Two-Link Mechanism With an Improved OPCL Method

HAN Qing-kai, ZHAO Xue-yan, WEN Bang-chun

2008, 29(12): 1417-1425.

Abstract(2937) PDF(722)

Abstract:
An improved OPCL method was developed and applied to both the small swing and the giant rotation synchronization of a two-link mechanism.Transition processes of the two kinds of synchronization were also discussed.Comparisons of different motion characteristics of the two-link synchronizations and the effects of different control parameters on the synchronous processes were investigated through numerical simulations.

On the Critical Velocity of the Sandwich Cylindrical Shell to Moving Internal Pressure

ZHOU Jia-xi, DENG Zi-chen, HOU Xiu-hui

2008, 29(12): 1426-1434.

Abstract(3185) PDF(703)

Abstract:
The critical velocity of the infinite long sandwich shell to moving internal pressure is studied using sandwich shell theory and elastodynamics theory.Firstly the propagation of axisymmetric free harmonic waves in the sandwich shell was studied using sandwich shell theory considering the compressibility of core and the transverse shear deformation of core and face sheets.Secondly on the basis of elastodynamics theory,the displacement components expanded by Legendre polynomials,as well as position-dependent elastic constants and densities were introduced into the equations of motion.The critical velocity is the minimum phase velocity on the desperation relation curve obtained using the two methods.Finally the numerical ex amples and FE simulations were executed.Results show that the tow critical velocities agree well with each other,and two desperation relation curves agree well with each other when wave number k is relatively small;however two limit phase velocities approach the shear wave velocities of the face sheet and the core respectively when k limits to infinite.The two methods are efficient to investigate wave propagation in the sandwich cylindrical shell,when k is relatively small.The critical velocity predicted by FE simulations agrees well with that predicted by theoretical analysis.

Mixed Time Discontinuous Space-Time Finite Element Method for Convection Diffusion Equations

LIU Yang, LI Hong, HE Siriguleng

2008, 29(12): 1435-1442.

Abstract(3109) PDF(539)

Abstract:
A mixed time discontinuous space-time finite element scheme for second order convection diffusion problems is constructed and analyzed.The order of the equation was lowered by mixed finite element method. And the low order equation was discretized by space-time finite element method,continuous in space but discontinuous in time.The stability,existence,uniqueness and convergence of the approximate solutions were proved.Finally,numerical results were presented to illustrate the efficiency of the method.

A New Matrix Method for Analyzing Vibration and Damping Effect of a Sandwich Circular Cylindrical Shell With a Viscoelastic Core

XIANG Yu, HUANG Yu-ying, LU Jing, YUAN Li-yun, ZOU Shi-zhi

2008, 29(12): 1443-1456.

Abstract(2889) PDF(724)

Abstract:
Based on the linear theories of thin cylindrical shells and viscoelastic materials,the governing equation describing vibration of a sandwich circular cylindrical shell with a viscoelastic core under harmonic excitation,which can be written in a matrix differential equation of first order,was derived by considering the energy dissipation due to the shear deformation of the viscoelastic core layer and the interaction between all layers.After that a new matrix method for solving this governing equation was established by means of the extended homogeneous capacity precision integration approach presented by authors.With these,the vibration characteristics and damping effect of the sandwich cylindrical shell can be studied.Its difference from the existing transfer matrix method is that the state vector in governing equation is composed of the displacements and internal forces of the sandwich shell rather than of the displacements and their derivatives.So the present method can be applied to solve the dynamic problems of the kind of sandwich shell with various boundary conditions and partially constrained layer damping.Numerical examples show that the proposed approach is very effective and reliable.

Elastic and Viscoelastic Solutions for Rotating Functionally Graded Hollow and Solid Cylinders

A. M. Zenkour, K. A. Elsibai, D. S. Mashat

2008, 29(12): 1457-1471.

Abstract(3127) PDF(572)

Abstract:
Analytical solutions for rotating functionally graded hollow and solid long cylinders are developed. Young's modulus and material density of the cylinder are assumed to vary exponentially through the radial direction and Poisson's ratio was assumed to be constant.A unified governing equation was derived from the equilibrium equations,compatibility equation,deformation theory of elasticity and the stress-strain relationships.The governing second-order differential equation was solved in terms of a hypergeometric function for the elastic deformation of rotating functionally graded cylinders.Dependence of stresses in the cylinder on the inhomogeneous parameters,geometry and boundary conditions was examined and discussed.Proposed solution was validated by comparing the results for rotating functionally graded hollow and solid cylinders to the results for rotating homogeneous isotropic cylinders.In addition,a viscoelastic solution for the rotating viscoelastic cylinder was presented.Moreover,the dependence of stresses in hollow and solid cylinders on the time parameter was examined.

A New Analytical Solution for Axisymmetric Biot’s Consolidation of a Finite Soil Layer

AI Zhi-yong, WANG Quan-sheng

2008, 29(12): 1472-1478.

Abstract(2917) PDF(677)

Abstract:
A new analytical method is presented to study the axis-symmetric Biot's consolidation of a finite soil layer.Starting from the governing equations of axis-symmetric Biot's consolidation,and based on the property of the Laplace transform,the relationship of basic variables for a point of a finite soil layer was established between the ground surface(z=0) and the depth z in the Laplace and Hankel transform domain.Combined with the boundary conditions of the finite soil layer,the analytical solution of any point in the transform domain can be obtained.The actual solution in the physical domain can be acquired by inverting the Laplace and the Hankel transforms.The numerical analysis for the axis-symmetric consolidation of a finite soil layer was carried out by program.

Consideration of Transient Heat Conduction in a Semi-Infinite Medium Using Homotopy Analysis Method

A. Rezania, A. Ghorbali, G. Domairry, H. Bararnia

2008, 29(12): 1479-1485.

Abstract(2765) PDF(562)

Abstract:
Transient heat conduction in a semi-infinite medium was considered for its many applications in various heat fields.Here,homotopy analysis method(HAM) was applied to solve this problem and analytical results were compared with those of exact and integral methods results.The results show that HAM can give much better approximations than the other approx imate methods.Change of heat fluxes and profiles of temperature are obtained in different times and positions for copper,iron and aluminum.

Optimal Distribution of Reliability for Large Network Based on Connectivity

CHEN Ling-li, YU Jie

2008, 29(12): 1486-1494.

Abstract(2789) PDF(533)

Abstract:
It is a non-polynomial complexity problem to calculate the connectivity of the complex network. When the reliability of the system can not be expressed as the function of the element reliability,some heuristic methods were applied to do the optimization based on connectivity of the network.The calculation structure of connectivity of complex network was analysed.The coefficient matrixes of Taylor second order expansion of the system connectivity was generated based on the calculation structure of connectivity of complex network.A optimal schedule is achieved based on genetic algorithms(GA).The fitness of seeds was calculated using the Taylor expansion function of system connectivity.The precise connectivity of the optimal schedule and the Taylor expansion function of system connectivity can be achieved by the approved Minty method or the recursive decomposition algorithm.When the error between the approximate connectivity and the precise value exceeds the assigned precision,optimize process was continued using GA and the Taylor function of system connectivity need renewal.The optimum process was called iterative GA.One case is illustrated iterative GA which can be used in the large network for optimal reliability attribution.One temporary optimal result will be generated every time in iteration process.These temporary optimal results approach the real optimal results.They can be regarded as the group of the approx imate optimal results that is useful in the real project.

An Analytic Solution to the Unsymmetrical Bending Problem of Diaphragm Coupling

ZHU Ke-ke, ZHU Ru-peng

2008, 29(12): 1495-1501.

Abstract(2582) PDF(603)

Abstract:
As the rigidity of either the hub or rim of the diaphragm coupling is much larger than that of the disk,and the unsymmetrical bending is under the condition of high speed revolution,a hypothesis was supposed that each circle in the middle plane before deformation remains its radius unchangeable after deformation but the plane on which the circle lies has a varying deflecting angle.Upon this and through the principle of energy variation,the corresponding Euler's equation,which has the primary integral,can be obtained.After some subsidiary factors were neglected,the analytic solution was achieved.Applying these formulas to a hyperbolic model of diaphragm,the results show that the octahedral shear stress varying less along either radial or thickness direction,but fluctuated greatly and periodically along circumferential direction,thus the unsymmetrical bending affects the material's fatigue significantly.

Sensitivity Analysis Method of Soil Parameters Based on Interval

SU Jing-bo, SHAO Guo-jian, CHU Wei-jiang

2008, 29(12): 1502-1512.

Abstract(2816) PDF(675)

Abstract:
Interval analysis method is a new uncertainty analysis method for engineering structures.A new sensitivity analysis method of engineering parameters was gained by introducing interval analysis method.And this will widen the application domain of interval analysis method.The interval analysis process of sensitivity factor matrix of soil parameters was given.The choosing method of the parameter intervals and decision-making target intervals was given according to interval analysis method.During the process of FEM,the secondary developments were done for Marc and the Duncan-Chang nonlinear elastic model and the mutual transfer between FORTRAN and MARC were implemented.By the engineering example,the rationality and feasibility were validated.And the conclusion was compared with that of the literatures.