Table of Content

01 December 2008, Volume 29 Issue 12

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Articles

A new method for computing laminar-turbulent transition and turbulence in compressible boundary layers---PSE+DNS

DONG Ming;ZHANG Yong-ming;ZHOU Heng

2008, 29(12):  1527-1534 .  doi:10.1007/s10483-008-1201-z

Abstract ( 1835 )   PDF (405KB) ( 1005 )  

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A new method for computing laminar-turbulent transition and turbulence in compressible boundary layers is proposed. It is especially useful for 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, is computed by parabolized stability equations (PSE). The direct numerical simulation (DNS) method is used to compute the transition process and turbulent flow, for which the inflow condition is 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 with this method agree well with those obtained by using only DNS method for the whole process. The computational cost of the proposed method is much less than using only DNS method.

Solution of two-dimensional scattering problem in piezoelectric/piezomagnetic media using a polarization method

HU Yang-fan;WANG Biao

2008, 29(12):  1535-1552 .  doi:10.1007/s10483-008-1202-x

Abstract ( 1692 )   PDF (356KB) ( 948 )  

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Using a 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 a two-dimensional piezoelectric/piezomagnetic "comparison body" is formulated. For simple harmonic motion, kernel of the polarization method reduces to a 2-D time-harmonic Green's function, which is obtained using the Radon transform. The expression is further simplified under conditions of low frequency of the incident wave and small diameter of the inclusion. Some analytical expressions are obtained. The analytical solutions for generalized piezoelectric/piezomagnetic anisotropic composites are given followed by simplified results for piezoelectric composites. Based on the latter results, two numerical results are provided for an elliptical cylindrical inclusion in a PZT-5H-matrix, showing the effect of different factors including size, shape, material properties, and piezoelectricity 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):  1553-1559 .  doi:10.1007/s10483-008-1203-x

Abstract ( 1695 )   PDF (199KB) ( 1030 )  

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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 increasing strain or strain-rate sensitivity index. The classical plastic-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):  1561-1568 .  doi:10.1007/s10483-008-1204-z

Abstract ( 1549 )   PDF (227KB) ( 874 )  

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An improved OPCL method is developed and applied to both small swing and giant rotation synchronization of a two-link mechanism. Transition processes of the two kinds of synchronization are discussed. Comparisons of different motion characteristics of the two-link synchronization and the effects of
different control parameters on synchronous processes are investigated with numerical simulations.

Critical velocity of sandwich cylindrical shell under moving internal pressure

ZHOU Jia-xi;DENG Zi-chenHOU Xiu-hui

2008, 29(12):  1569-1578 .  doi:10.1007/s10483-008-1205-y

Abstract ( 1887 )   PDF (273KB) ( 1121 )  

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Critical velocity of an infinite long sandwich shell under moving internal pressure is studied using the sandwich shell theory and elastodynamics theory. Propagation of axisymmetric free harmonic waves in the sandwich shell is studied using the sandwich shell theory by considering compressibility and transverse shear deformation of the core, and transverse shear deformation of face sheets. Based on the elastodynamics theory, displacement components expanded by Legendre polynomials, and position-dependent elastic constants and densities are introduced into the equations of motion. Critical velocity is the minimum phase velocity on the desperation relation curve obtained by using the two methods. Numerical examples and the finite element (FE) simulations are presented. The results show that the two critical velocities agree well with each other, and two desperation relation curves agree well with each other when the wave number k is relatively small. However, two limit phase velocities approach to the shear wave velocities of the face sheet and the core respectively when k limits to infinite. The two methods are efficient in the investigation of wave propagation in a sandwich cylindrical shell when k is relatively small. The critical velocity predicted in the FE simulations agrees with theoretical prediction.

Mixed time discontinuous space-time finite element method for convection diffusion equations

LIU Yang;LI Hong;HE Siriguleng

2008, 29(12):  1579-1586 . 

Abstract ( 1793 )   PDF (244KB) ( 993 )  

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A mixed time discontinuous space-time finite element scheme for second-order convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order equation is discretized with a space-time finite element method, continuous in space but discontinuous in time. Stability, existence, uniqueness and convergence of the approximate solutions are proved. Numerical results are presented to illustrate efficiency of the proposed method.

New matrix method for analyzing vibration and damping effect of sandwich circular cylindrical shell with viscoelastic core

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

2008, 29(12):  1587-1600 .  doi:10.1007/s10483-008-1207-x

Abstract ( 1755 )   PDF (373KB) ( 1073 )  

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Based on the linear theories of thin cylindrical shells and viscoelastic materials, a governing equation describing vibration of a sandwich circular cylindrical shell with a viscoelastic core under harmonic excitation is derived. The equation can be written as a matrix differential equation of the first order, and is obtained by considering the energy dissipation due to the shear deformation of the viscoelastic core layer and the interaction between all layers. A new matrix method for solving the governing equation is then presented with an extended homogeneous capacity precision integration approach. Having obtained these, vibration characteristics and damping effect of the sandwich cylindrical shell can be studied. The method differs from a recently published work as the state vector in the governing equation is composed of displacements and internal forces of the sandwich shell rather than displacements and their derivatives. So the present method can be applied to solve dynamic problems of the kind of sandwich shells with various boundary conditions and partially constrained layer damping. Numerical examples show that the proposed approach is effective and reliable compared with the existing methods.

Elastic and viscoelastic solutions to rotating functionally graded hollow and solid cylinders

A. M. Zenkour;K. A. Elsibai and D. S. Mashat

2008, 29(12):  1601-1616 .  doi:10.1007/s10483-008-1208-x

Abstract ( 2037 )   PDF (445KB) ( 1034 )  

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Analytical solutions to rotating functionally graded hollow and solid long cylinders are developed. Young's modulus and material density of the cylinder are assumed to vary exponentially in the radial direction, and Poisson's ratio is assumed to be constant. A unified governing equation is derived from the equilibrium equations, compatibility equation, deformation theory of elasticity and the stress-strain relationship. The governing second-order differential equation is 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 is examined and discussed. The proposed solution is validated by comparing the results for rotating functionally graded hollow and solid cylinders with the results for rotating homogeneous isotropic cylinders. In addition, a viscoelastic solution to the rotating viscoelastic cylinder is presented, and dependence of stresses in hollow and solid cylinders on the time parameter is examined.

A new analytical solution to axisymmetric Biot's consolidation of a finite soil layer

AI Zhi-yong;WANG Quan-sheng

2008, 29(12):  1617-1624 .  doi:10.1007/s10483-008-1209-9

Abstract ( 1764 )   PDF (257KB) ( 1704 )  

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A new analytical method is presented to study the axisymmetric Biot's consolidation of a finite soil layer. Starting from the governing equations of axisymmetric Biot's consolidation, and based on the property of Laplace transform, the relation of basic variables for a point of a finite soil layer is established between the ground surface (z= 0) and the depth z in the Laplace and Hankel transform domains. 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 obtained by inverse Laplace and Hankel transforms. A numerical analysis for the axisymmetric consolidation of a finite soil layer is carried out.

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):  1625-1632 .  doi:10.1007/s10483-008-1210-3

Abstract ( 1717 )   PDF (236KB) ( 1120 )  

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In the current work, transient heat conduction in a semi-infinite medium is considered for its many applications in various heat fields. Here, the homotopy analysis method (HAM) is applied to solve this problem and analytical results are compared with those of the exact and integral methods
results. The results show that the HAM can give much better approximations than the other approximate methods. Changes in heat fluxes and profiles of temperature are obtained at different times and positions for copper, iron and aluminum.

Optimal distribution of reliability for a large network based on connectivity

CHEN Ling-li;YU Jie

2008, 29(12):  1633-1642 .  doi:10.1007/s10483-008-1211-z

Abstract ( 1766 )   PDF (223KB) ( 677 )  

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It is a non-polynomial complexity problem to calculate connectivity of the complex network. When the system reliability cannot be expressed as a function of element reliability, we have to apply some heuristic methods for optimization based on connectivity of the network. The calculation structure of connectivity of complex network is analyzed in the paper. The coefficient matrixes of Taylor second order expansion of the system connectivity is generated based on the calculation structure of connectivity of complex network. An optimal schedule is achieved based on genetic algorithms (GA). Fitness of seeds is calculated using the Taylor expansion function of system connectivity. 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 error between approximate connectivity and the precise value exceeds the assigned value, the optimization process is continued using GA, and the Taylor function of system connectivity needs to be renewed. The optimization process is called iterative GA. Iterative GA can be used in the large network for optimal reliability attribution. One temporary optimal result will be generated every time in the iteration process. These temporary optimal results approach the real optimal results. They can be regarded as a group of approximate optimal results useful in the real project.

An analytic solution to asymmetrical bending problem of diaphragm coupling

ZHU Ke-ke;ZHU Ru-peng

2008, 29(12):  1643-1649 .  doi:10.1007/s10483-008-1212-y

Abstract ( 1610 )   PDF (225KB) ( 906 )  

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Because rigidity of either hub or rim of diaphragm coupling is much greater than that of the disk, and asymmetrical bending is under the condition of high speed revolution, an assumption is made that each circle in the middle plane before deformation keeps its radius unchanged after deformation, but the plane on which the circle lies has a varying deflecting angle. Based on this assumption, and according to the principle of energy variation, the corresponding Euler's equation can be obtained, which has the primary integral. By neglecting some subsidiary factors, an analytic solution is obtained. Applying these formulas to a hyperbolic model of diaphragm, the results show that the octahedral shear stress varies less along either radial or thickness direction, but fluctuates greatly and periodically along circumferential direction. Thus asymmetrical bending significantly affects the material's fatigue.

Sensitivity analysis of soil parameters based on interval

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

2008, 29(12):  1651-1662 .  doi:10.1007/s10483-008-1213-y

Abstract ( 1739 )   PDF (245KB) ( 1304 )  

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Interval analysis is a new uncertainty analysis method for engineering structures. In this paper, a new sensitivity analysis method is presented by introducing interval analysis which can expand applications of the interval analysis method. The interval analysis process of sensitivity factor matrix of soil parameters is given. A method of parameter intervals and decision-making target intervals is given according to the interval analysis method. With FEM, secondary developments are done for Marc and the Duncan-Chang nonlinear elastic model. Mutual transfer between FORTRAN and Marc is implemented. With practial examples, rationality and feasibility are validated. Comparison is made with some published results.