Table of Content

03 July 2008, Volume 29 Issue 7

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Articles

PSE as applied to problems of transition in compressible boundary layers

ZHANG Yong-ming;ZHOU Heng;

2008, 29(7):  833-840 .  doi:10.1007/s10483-008-0701-8

Abstract ( 1867 )   PDF (353KB) ( 836 )  

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A new idea of using the parabolized stability equation (PSE) method to predict laminar-turbulent transition is proposed. It is tested in the prediction of thelocation of transition for compressible boundary layers on flat plates, and the results are compared with those obtained by direct numerical simulations (DNS). The agreement is satisfactory, and the reason for this is that the PSE method faithfully reproduces the mechanism leading to the breakdown process in laminar-turbulent transition, i.e., the modification of mean flow profile leads to a remarkable change in its stability characteristics.

Elasto-plastic postbuckling of damaged orthotropic plates

TIAN Yan-ping;FU Yi-ming

2008, 29(7):  841-853 .  doi:10.1007/s10483-008-0702-y

Abstract ( 1497 )   PDF (311KB) ( 815 )  

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Based on the elasto-plastic mechanics and continuum damage theory, a yield criterion related to spherical tensor of stress is proposed to describe the mixed hardening of damaged orthotropic materials. Its dimensionless form is isomorphic with the Mises criterion for isotropic materials. Furthermore, the
incremental elasto-plastic damage constitutive equations and damage
evolution equations are established. Based on the classical nonlinear plate theory, the incremental nonlinear equilibrium equations of orthotropic thin plates considering damage effect are obtained, and solved with the finite difference and iteration methods. In the numerical examples, the effects of damage evolution and initial deflection on the elasto-plastic postbuckling of
orthotropic plates are discussed in detail.

From the second gradient operator and second class of integral theorems to Gaussian or spherical mapping invariants

YIN Ya-jun;WU Ji-ye;HUANG Ke-zhi;FAN Qin-shan

2008, 29(7):  855-862 .  doi:10.1007/s10483-008-0703-1

Abstract ( 1595 )   PDF (177KB) ( 767 )  

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By combining of the second gradient operator, the second class of integral theorems, the Gaussian-curvature-based integral theorems and the Gaussian (or spherical) mapping, a series of invariants or geometric conservation
quantities under Gaussian (or spherical) mapping are revealed. From
these mapping invariants important transformations between original
curved surface and the spherical surface are derived. The potential
applications of these invariants and transformations to geometry are
discussed.

Interaction between collinear periodic cracks in an infinite piezoelectric body

CUI Zhi-jian;HU Hong-ping;YANG Feng

2008, 29(7):  863-870 .  doi:10.1007/s10483-008-0704-x

Abstract ( 1479 )   PDF (177KB) ( 739 )  

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The problem of collinear periodic cracks in an infinite piezoelectric body is studied. Effect of saturation strips at the crack-tips is taken into account. By means of the Stroh formalism and the conformal mapping technique, the
general periodic solutions for collinear cracks are obtained. The stress intensity factors and the size of saturation strips are derived analytically, and their dependencies on the ratio of the periodicity on the half-length of the crack are analyzed in detail. Numerical results show the following two facts. (1) When h/l>4.0, the stress intensity factors become almost identical to those of a single crack in an infinite piezoelectric body. This indicates that the interaction between cracks can be ignored in establishing the criterion for the crack initiation in this case. (2) The speed of the saturation strip size of periodic cracks approaching that of a single crack depends on the electric load applied at infinity. In general, a large electric load at infinity is associated with a slow approaching speed.

Study of numerical errors in direct numerical simulation and\\ large eddy simulation

YANG Xiao-long;FU Song

2008, 29(7):  871-880 .  doi:10.1007/s10483-008-0705-x

Abstract ( 1546 )   PDF (312KB) ( 627 )  

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By comparing the energy spectrum and total kinetic energy, the effects of numerical errors (which arise from aliasing and discretization errors), subgrid-scale (SGS) models, and their interactions on direct numerical simulation (DNS)
and large eddy simulation (LES) are investigated. The decaying isotropic turbulence is chosen as the test case. To simulate complex geometries, both the spectral method and Padé compact difference schemes are studied. The truncated Navier-Stokes (TNS) equation model with Padé discrete filter is adopted as the SGS model. It is found that the discretization error plays a key role in DNS. Low order difference schemes may be unsuitable. However, for LES, it is found that the SGS model can represent the effect of small scales to
large scales and dump the numerical errors. Therefore, reasonable results can also be obtained with a low order discretization scheme.

A stencil-like volume of fluid (VOF) method for tracking free interface

LI Xiao-wei;FAN Jun-fei

2008, 29(7):  881-888 . 

Abstract ( 1710 )   PDF (185KB) ( 875 )  

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A stencil-like volume of fluid (VOF) method is proposed for tracking free interface. A stencil on a grid cell is worked out according to the normal direction of the interface, in which only three interface positions are possible in
2D cases, and the interface can be reconstructed by only requiring the known local volume fraction information. On the other hand, the fluid-occupying-length is defined on each side of the stencil, through which a unified fluid-occupying volume model and a unified algorithm can be obtained to solve the interface advection equation. The method is suitable for the arbitrary geometry of the grid cell, and is extendible to 3D cases. Typical numerical examples show that the current method can give "sharp" results for tracking free interface.

Large deflection of circular membrane under concentrated force

JIN Cong-rui

2008, 29(7):  889-896 .  doi:10.1007/s10483-008-0707-x

Abstract ( 2054 )   PDF (105KB) ( 1355 )  

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The analytical solution to a Föppl-Hencky membrane with a rigidly clamped boundary condition under concentrated force is provided. Stability of a nonlinear circular membrane is investigated.

A Boussinesq model with alleviated nonlinearity and dispersion

ZHANG Dian-xin;TAO Jian-hua

2008, 29(7):  897-908 .  doi:10.1007/s10483-008-0708-6

Abstract ( 2035 )   PDF (277KB) ( 637 )  

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The classical Boussinesq equation is a weakly nonlinear and weakly dispersive equation, which has been widely applied to simulate wave propagation in off-coast shallow waters. A new form of the Boussinesq model for an uneven bottoms is derived in this paper. In the new model, nonlinearity is reduced
without increasing the order of the highest derivative in the differential equations. Dispersion relationship of the model is improved to the order of Padé (2,2) by adjusting a parameter in the model based on the long wave approximation. Analysis of the linear dispersion, linear shoaling and nonlinearity of the present model shows that the performances in terms of nonlinearity, dispersion and shoaling of this model are improved. Numerical
results obtained with the present model are in agreement with experimental data.

Three kinds of nonlinear dispersive waves in elastic rods with finite deformation

ZHANG Shan-yuan;LIU Zhi-fang

2008, 29(7):  909-917 .  doi:10.1007/s10483-008-0709-2

Abstract ( 1713 )   PDF (147KB) ( 889 )  

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On the basis of classical linear theory on longitudinal, torsional and flexural waves in thin elastic rods, and taking finite deformation and dispersive effects into consideration, three kinds of nonlinear evolution equations are derived. Qualitative analysis of three kinds of nonlinear equations are presented. It is shown that these equations have homoclinic or heteroclinic orbits on the phase plane, corresponding to solitary wave or shock wave solutions, respectively. Based on the principle of homogeneous balance, these equations are solved with the Jacobi elliptic function expansion method. Results show that existence of solitary wave solution and shock wave solution is possible under certain conditions. These conclusions are consistent with qualitative analysis.

Field structure at mode III dynamically propagating crack tip in elastic-viscoplastic materials

JIA Bin;WANG Zhen-qing;LI Yong-dong

2008, 29(7):  919-925 .  doi:10.1007/s10483-008-0710-x

Abstract ( 1739 )   PDF (185KB) ( 581 )  

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An elastic-viscoplastic mechanics model is used to investigate asymptotically the mode III dynamically propagating crack tip field in elastic-viscoplastic materials. The stress and strain fields at the crack tip possess the same power-law singularity under a linear-hardening condition. The singularity
exponent is uniquely determined by the viscosity coefficient of the material. Numerical results indicate that the motion parameter of the crack propagating speed has little effect on the zone structure at the crack tip. The hardening
coefficient dominates the structure of the crack-tip field. However, the secondary plastic zone has little influence on the field. The viscosity of the material dominates the strength of stress and strain fields at the crack tip while it does have certain influence on the crack-tip field structure. The dynamic crack-tip field degenerates into the relevant quasi-static solution when the crack moving speed is zero. The corresponding perfectly-plastic
solution is recovered from the linear-hardening solution when the hardening coefficient becomes zero.

Multi-symplectic method for generalized Boussinesq equation

HU Wei-peng;DENG Zi-chen;

2008, 29(7):  927-932 .  doi:10.1007/s10483-008-0711-3

Abstract ( 1766 )   PDF (281KB) ( 774 )  

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The generalized Boussinesq equation that represents a group of important nonlinear equations possesses many interesting properties. Multi-symplectic formulations of the generalized Boussinesq equation in the Hamilton space are introduced in this paper. And then an implicit multi-symplectic scheme
equivalent to the multi-symplectic Box scheme is constructed to solve the partial differential equations (PDEs) derived from the generalized Boussinesq equation. Finally, the numerical experiments on the soliton solutions of the generalized Boussinesq equation are reported. The results show that the multi-symplectic method is an efficient algorithm with excellent long-time numerical behaviors for nonlinear partial differential equations.

Exact solution for warping of spatial curved beams in natural coordinates

ZHU Li-li;ZHAO Ying-hua

2008, 29(7):  933-941 .  doi:10.1007/s10483-008-0712-x

Abstract ( 1830 )   PDF (222KB) ( 1014 )  

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The purpose of the paper is to present an exact analytical solution of a spatial curved beam under multiple loads based on the existing theory. The transverse shear deformation and torsion-related warping effects are taken into account. By using this solution, a plane curved beam subjected to uniform vertical loads and torsions is analyzed. Accuracy and efficiency of present
theory are demonstrated by comparing its numerical results with Heins' solution. Furthermore, the effects of the transverse shear deformation and torsion-related warping on deformation of the beam are discussed.

Viscous flow with free surface motion by least square finite element method

TANG Bo;LI Jun-feng;WANG Tian-shu

2008, 29(7):  943-952 .  doi:10.1007/s10483-008-0713-x

Abstract ( 1771 )   PDF (1084KB) ( 882 )  

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A method for simulation of free surface problems is presented. Based on the viscous incompressible Navier-Stokes equations, space discretization of the flow is obtained by the least square finite element method. The time evolution is obtained by the finite difference method. Lagrangian description is used to track the free surface. The results are compared with the experimental dam break results, including water collapse in a 2D rectangular section and in a 3D cylinder section. A good agreement is achieved for the distance of surge front as well as the height of the residual column.

A note on Block H-matrices and spectrum of block

LIU Jian-zhou;HUANG Ze-jun

2008, 29(7):  953-960 .  doi:10.1007/s10483-008-0714-y

Abstract ( 1604 )   PDF (113KB) ( 637 )  

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In this paper, we make further discussions and improvements on the results presented in the previously published work ``Block H-matrices and spectrum of block matrices''. Furthermore, a new bound for eigenvalues of block matrices is given with examples to show advantages of the new result.

Temperature field at time of pulse current discharge in metal structure

FU Yu-ming;TIAN Zhen-guo;ZHENG Li-juan;LI Wei

2008, 29(7):  961-966 .  doi:10.1007/s10483-008-0715-y

Abstract ( 1623 )   PDF (137KB) ( 727 )  

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Theoretical analysis is made on the temperature field at the time of pulse current discharge in a metal structure with an elliptical embedding crack. In finding the temperature field, analogy between the current flow through an
elliptical embedding crack and the fluid flow through a barrier is made based on the similarity principle. Boundary conditions derived from this theory are introduced so that the distribution of current density and the temperature field expressions can be obtained. The study provides a theoretic basis to the applications of stopping spatial crack with electromagnetic heating.

Several properties of new ellipsoids

SHEN Ya-jun;YUAN Jun

2008, 29(7):  967-973 .  doi:10.1007/s10483-008-0716-y

Abstract ( 1508 )   PDF (107KB) ( 564 )  

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We first characterize a polytope whose new ellipsoid is a ball. Furthermore, we prove some properties for the operator Γ^_-2 and obtain some inequalities.