Table of Content

23 December 2009, Volume 30 Issue 12

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Articles

Second-order sensitivity of eigenpairs in multiple parameter structures

CHEN Su-Huan;GUO Rui;MENG Guang-Wei

2009, 30(12):  1475.  doi:10.1007/s10483-009-1201-z

Abstract ( 1384 )   PDF (247KB) ( 1036 )  

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This paper presents methods for computing a second-order sensitivity matrix and the Hessian matrix of eigenvalues and eigenvectors of multiple parameter structures. Second-order perturbations of eigenvalues and eigenvectors are transformed into multiple parameter forms, and the second-order perturbation sensitivity matrices of eigenvalues and eigenvectors are developed. With these formulations, the efficient methods based on the second-order Taylor expansion and second-order perturbation are obtained to estimate changes of eigenvalues and eigenvectors when the design parameters are changed. The presented method avoids direct differential operation, and thus reduces difficulty for computing the second-order sensitivity matrices of eigenpairs. A numerical example is given to demonstrate application and accuracy of the proposed method.

Crack-tip field on mode II interface crack of double dissimilar orthotropic composite materials

ZHANG Xue-Xia;CUI Xiao-Chao;YANG Wei-Yang;LI Jun-Lin

2009, 30(12):  1489-1504.  doi:10.1007/s10483-009-1202-4

Abstract ( 1711 )   PDF (341KB) ( 1075 )  

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Two systems of non-homogeneous linear equations with 8 unknowns are obtained. This is done by introducing two stress functions containing 16 undetermined coefficients and two real stress singularity exponents with the help of boundary conditions. By solving the above systems of non-homogeneous linear equations, the two real stress singularity exponents can be determined when the double material parameters meet certain conditions. The expression of the stress function and all coefficients are obtained based on the uniqueness theorem of limit. By substituting these parameters into the corresponding mechanics equations, theoretical solutions to the stress intensity factor, the stress field and the displacement field near the crack tip of each material can be obtained when both discriminants of the characteristic equations are less than zero. Stress and displacement near the crack tip show mixed crack characteristics without stress oscillation and crack surface overlapping. As an example, when the two orthotropic materials are the same, the stress singularity exponent, the stress intensity factor, and expressions for the stress and the displacement fields of the orthotropic single materials can be derived.

Effect of rotation in generalized thermoelastic solid under the influence of gravity with an overlying infinite thermoelastic fluid

Praveen Ailawalia;Naib Singh Narah

2009, 30(12):  1505.  doi:10.1007/s10483-009-1203-6

Abstract ( 1796 )   PDF (318KB) ( 1109 )  

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The present problem is concerned with the study of deformation of a rotating generalized thermoelastic solid with an overlying infinite thermoelastic fluid due to different forces acting along the interface under the influence of gravity. The components of displacement, force stress, and temperature distribution are first obtained in Laplace and Fourier domains by applying integral transforms, and then obtained in the physical domain by applying a numerical inversion method. Some particular cases are also discussed in the context of the problem. The results are also presented graphically to show the effect of rotation and gravity in the medium.

A novel four-node quadrilateral element with continuous nodal stress

TANG Xu-Hai;ZHENG Chao;WU Sheng-Chuan;ZHANG Jian-Hai

2009, 30(12):  1519.  doi:10.1007/s10483-009-1204-1

Abstract ( 1657 )   PDF (1057KB) ( 1443 )  

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Formulation and numerical evaluation of a novel four-node quadrilateral element with continuous nodal stress (Q4-CNS) are presented. Q4-CNS can be regarded as an improved hybrid FE-meshless four-node quadrilateral element (FE-LSPIM QUAD4), which is a hybrid FE-meshless method. Derivatives of Q4-CNS are continuous at nodes, so the continuous nodal stress can be obtained without any smoothing operation. It is found that, compared with the standard four-node quadrilateral element (QUAD4), Q4-CNS can achieve significantly better accuracy and higher convergence rate. It is also found that Q4-CNS exhibits high tolerance to mesh distortion. Moreover, since derivatives of Q4-CNS shape functions are continuous at nodes, Q4-CNS is potentially useful for the problem of bending plate and shell models.

Numerical method of Rayleigh-Stokes problem for heated generalized second grade fluid with fractional derivative

ZHUANG Ping-Hui;LIU Qing-Xia

2009, 30(12):  1533.  doi:10.1007/s10483-009-1205-7

Abstract ( 1924 )   PDF (432KB) ( 1065 )  

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In this paper, we consider the Rayleigh-Stokes problem for a heated generalized second grade fluid (RSP-HGSGF) with fractional derivative. An effective numerical method for approximating RSP-HGSGF in a bounded domain is presented. The stability and convergence of the method are analyzed. Numerical examples are presented to show the application of the present technique.

Numerical study of macroscopical drainage process in fabricating foamed aluminum using microscopical method

LI Ke;XIE Mao-Zhao;LIU Hong

2009, 30(12):  1547.  doi:10.1007/s10483-009-1206-x

Abstract ( 1389 )   PDF (404KB) ( 879 )  

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The velocity field in a single Plateau border (PB) of the aluminum foam in the drainage process is studied using a mathematical model for the flow inside a microchannel. We show that the liquid/gas interface mobility characterized by the Newtonian surface viscosity has a substantial effect on the velocity inside the single PB. With the same liquid/gas interfacial mobility and the same radius of the curvature, the maximum velocity inside an exterior PB is about 6 ∼ 8 times as large as that inside an interior PB. We also find a critical value of the interfacial mobility in the interior PB. For the values greater and less than this critical value, the effects of the film thickness on the velocity in the PB show opposite tendencies. Based on the multiscale methodology, with the coupling between the microscale and the macroscale and the results obtained from the microscopical model, a simplified macroscopical drainage model is presented for the aluminum foams. The comparisons among the computational results obtained from the present model, the experimental data quoted in the literature, and the results of the classical drainage equation show a reasonable agreement. The computational results reveal that the liquid holdup of the foams is strongly dependent on the value of the mobility and the bubble radius.

Numerical investigation on a transition prediction model

SUN Zhen-Xu;ZHAO Xiao-Li;SONG Jing-Jing;DU Te-Zhuan

2009, 30(12):  1559.  doi:10.1007/s10483-009-1207-z

Abstract ( 1522 )   PDF (344KB) ( 1039 )  

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A new transition prediction model is introduced, which couples the intermittency effect into the turbulence transport equations and takes the characteristics of fluid transition into consideration to mimic the exact process of transition. Test cases include a two-dimensional incompressible plate and a two-dimensional NACA0012 airfoil. Performance of this transition model for incompressible flows is studied, with numerical results consistent to experimental data. The requirement of grid resolution for this transition model is also studied.

MHD flow of a viscous fluid on a nonlinear porous shrinking sheet with homotopy analysis method

S. Nadeem;Anwar Hussain

2009, 30(12):  1569.  doi:10.1007/s10483-009-1208-6

Abstract ( 1640 )   PDF (307KB) ( 1584 )  

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The present paper investigates the magnetohydrodynamic (MHD) flow of a viscous fluid towards a nonlinear porous shrinking sheet. The governing equations are simplified by similarity transformations. The reduced problem is then solved by the homotopy analysis method. The pertinent parameters appearing in the problem are discussed graphically and presented in tables. It is found that the shrinking solutions exist in the presence of MHD. It is also observed from the tables that the solutions for f"(0) with different values of parameters are convergent.

A two-order and two-scale computation method for nonselfadjoint elliptic problems with rapidly oscillatory coefficients

SU Fang;CUI Jun-Zhi;XU Zhan

2009, 30(12):  1579.  doi:10.1007/s10483-009-1209-z

Abstract ( 1684 )   PDF (331KB) ( 1029 )  

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The purpose of this paper is to solve nonselfadjoint elliptic problems with rapidly oscillatory coefficients. A two-order and two-scale approximate solution expression for nonselfadjoint elliptic problems is considered, and the error estimation of the twoorder and two-scale approximate solution is derived. The numerical result shows that the presented approximation solution is effective.

Some results of variational inclusion problems and fixed point problems with applications

HAO Yan

2009, 30(12):  1589.  doi:10.1007/s10483-009-1210-x

Abstract ( 1690 )   PDF (163KB) ( 962 )  

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This paper introduces a general iterative algorithm to approximate a common element in the solution set of quasi-variational inclusion problems and the common fixed point set of an infinite family of nonexpansive mappings. It is proven that the iterative sequences generated in the proposed iterative algorithm converge strongly to some common element in the framework of the real Hilbert spaces.

Uniform attractors for non-autonomous Klein-Gordon-Schrödinger lattice systems

HUANG Jin-Wu;HAN Xiao-Ying;ZHOU Sheng-Fan

2009, 30(12):  1597.  doi:10.1007/s10483-009-1211-z

Abstract ( 1571 )   PDF (222KB) ( 1274 )  

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The existence of a compact uniform attractor for a family of processes corresponding to the dissipative non-autonomous Klein-Gordon-Schrödinger lattice dynamical system is proved. An upper bound of the Kolmogorov entropy of the compact uniform attractor is obtained, and an upper semicontinuity of the compact uniform attractor is established.