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2014年 第35卷 第10期    刊出日期：2014-10-01

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论文

Self-adaptive one-dimensional nonlinear finite element method based on element energy projection method

袁驷;杜炎;邢沁妍;叶康生

2014, 35(10):  1223-1232.  doi:10.1007/s10483-014-1869-9

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Stretching strongly confined semiflexible polymer chain

王记增;李润华

2014, 35(10):  1233-1238.  doi:10.1007/s10483-014-1862-9

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By the so-called wormlike chain (WLC) model in polymer physics envision- ing an isotropic rod that is continuously flexible, the force-extension relations of semi- flexible polymer chains strongly constrained by various confinements are theoretically investigated, including a slab-like confinement where the polymer chains are sandwiched between two parallel impenetrable walls, and a capped nanochannel confinement with a circular or rectangular cross-section where the chains are bounded in three directions. The Brownian dynamics (BD) simulations based on the generalized bead-rod (GBR) model are performed to verify the theoretical predictions.

Finite cell method compared to h-version finite element method for elasto-plastic problems

A. ABEDIAN;J. PARVIZIAN;A. D�STER;E. RANK

2014, 35(10):  1239-1248.  doi:10.1007/s10483-014-1861-9

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The finite cell method (FCM) combines the high-order finite element method (FEM) with the fictitious domain approach for the purpose of simple meshing. In the present study, the FCM is used to the Prandtl-Reuss flow theory of plasticity, and the results are compared with the h-version finite element method (h-FEM). The numerical results show that the FCM is more efficient compared to the h-FEM for elasto-plastic problems, although the mesh does not conform to the boundary. It is also demonstrated that the FCM performs well for elasto-plastic loading and unloading.

Strip-coalesced interior zone model for two unequal collinear cracks weakening piezoelectric media

R. R. BHARGAVA;K. JANGID

2014, 35(10):  1249-1260.  doi:10.1007/s10483-014-1890-9

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In this paper, a mathematical strip-saturation model is proposed for a poled transversely isotropic piezoelectric plate weakened by two impermeable unequal-collinear hairline straight cracks. Remotely applied in-plane unidirectional electromechanical loads open the cracks in mode-I such that the saturation zone developed at the interior tips of cracks gets coalesced. The developed saturation zones are arrested by distributing over their rims in-plane normal cohesive electrical displacement. The problem is solved using the Stroh formalism and the complex variable technique. The expressions are derived for the stress intensity factors (SIFs), the lengths of the saturation zones developed, the crack opening displacement (COD), and the energy release rate. An illustrative numerical case study is presented for the poled PZT-5H ceramic to investigate the effect of prescribed electromechanical loads on parameters affecting crack arrest. Also, the effect of different lengths of cracks on the SIFs and the local energy release rate (LERR) has been studied. The results obtained are graphically presented and analyzed.

Dynamic anti-plane analysis for two symmetrically interfacial cracks near circular cavity in piezoelectric bi-materials

A. HASSAN;宋天舒

2014, 35(10):  1261-1270.  doi:10.1007/s10483-014-1891-9

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The present paper is exposed theoretically to the influence on the dynamic stress intensity factor (DSIF) in the piezoelectric bi-materials model with two symmet- rically permeable interfacial cracks near the edges of a circular cavity, subjected to the dynamic incident anti-plane shearing wave (SH-wave). An available theoretical method to dynamic analysis in the related research field is provided. The formulations are based on Green's function method. The DSIFs at the inner and outer tips of the left crack are obtained by solving the boundary value problems with the conjunction and crack- simulation technique. The numerical results are obtained by the FORTRAN language program and plotted to show the influence of the variations of the physical parameters, the structural geometry, and the wave frequencies of incident wave on the dimensionless DSIFs. Comparisons with previous work and between the inner and outer tips are con- cluded.

Analysis of stress intensity factor in orthotropic bi-material mixed interface crack

赵文彬;张雪霞;崔小朝;杨维阳

2014, 35(10):  1271-1292.  doi:10.1007/s10483-014-1864-9

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Adopting the complex function approach, the paper studies the stress intensity factor in orthotropic bi-material interface cracks under mixed loads. With con- sideration of the boundary conditions, a new stress function is introduced to transform the problem of bi-material interface crack into a boundary value problem of partial dif- ferential equations. Two sets of non-homogeneous linear equations with 16 unknowns are constructed. By solving the equations, the expressions for the real bi-material elastic constant λ_t and the real stress singularity exponents ε_t are obtained with the bi-material engineering parameters satisfying certain conditions. By the uniqueness theorem of limit, undetermined coefficients are determined, and thus the bi-material stress intensity factor in mixed cracks is obtained. The bi-material stress intensity factor characterizes features of mixed cracks. When orthotropic bi-materials are of the same material, the degenerate solution to the stress intensity factor in mixed bi-material interface cracks is in complete agreement with the present classic conclusion. The relationship between the bi-material stress intensity factor and the ratio of bi-material shear modulus and the relationship be- tween the bi-material stress intensity factor and the ratio of bi-material Young's modulus are given in the numerical analysis.

Form invariance and conserved quantity for weakly nonholonomic system

吴惠彬;梅凤翔

2014, 35(10):  1293-1300.  doi:10.1007/s10483-014-1863-9

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The form invariance and the conserved quantity for a weakly nonholonomic system (WNS) are studied. The WNS is a nonholonomic system (NS) whose constraint equations contain a small parameter. The differential equations of motion of the system are established. The definition and the criterion of form invariance of the system are given. The conserved quantity deduced from the form invariance is obtained. Finally, an illustrative example is shown.

Oscillatory Couette flow of rotating Sisko fluid

T. HAYAT;S. ABELMAN;M. HAMESE

2014, 35(10):  1301-1310.  doi:10.1007/s10483-014-1865-9

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The oscillatory Couette flow of a magnetohydrodynamic (MHD) Sisko fluid between two infinite non-conducting parallel plates is explored in a rotating frame. The lower plate is fixed, and the upper plate is oscillating in its own plane. Using MATLAB, a numerical solution to the resulting nonlinear system is presented. The influence of the physical parameters on the velocity components is analyzed. It is found that the effect of rotation on the primary velocity is more significant than that on the secondary velocity. Further, the oscillatory character in the flow is also induced by rotation. The considered flow situation behaves inertialess when the Reynolds number is small.

Characteristic fractional step finite difference method for nonlinear section coupled system

袁益让;李长峰;孙同军;刘允欣

2014, 35(10):  1311-1330.  doi:10.1007/s10483-014-1869-9

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For the section coupled system of multilayer dynamics of fluids in porous media, a parallel scheme modified by the characteristic finite difference fractional steps is proposed for a complete point set consisting of coarse and fine partitions. Some tech- niques, such as calculus of variations, energy method, twofold-quadratic interpolation of product type, multiplicative commutation law of difference operators, decomposition of high order difference operators, and prior estimates, are used in theoretical analysis. Optimal order estimates in l² norm are derived to show accuracy of the second order approximation solutions. These methods have been used to simulate the problems of migration-accumulation of oil resources.

Hydromagnetic oscillatory Couette flow in rotating system with induced magnetic field

G. S. SETH;S. M. HUSSAIN;S. SARKAR

2014, 35(10):  1331-1344.  doi:10.1007/s10483-014-1868-9

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This paper presents a study of hydromagnetic Couette flow of an incompressible and electrically conducting fluid between two parallel rotating plates, one of which is oscillating in its own plane. A uniform transverse magnetic field is used, and the induced magnetic field is taken into account. The exact solution to the governing equations is obtained in a closed form. The solution to the problem in the case of vanishing and small finite magnetic Prandtl numbers is also derived from the general solution. The asymptotic behavior of the solution for large values of the frequency parameter is analyzed to gain some physical insights into the flow pattern. Expressions for the shear stress at both the oscillatory and stationary plates due to primary and secondary flows and mass flow rate in the primary and secondary flow directions are also obtained. The results of the fluid velocity and the induced magnetic field are presented. The shear stresses on the plates due to the primary and secondary flows and the corresponding mass flow rates are presented in a tabular form.

First-order optimality condition of basis pursuit denoise problem

朱玮;舒适;成礼智

2014, 35(10):  1345-1352.  doi:10.1007/s10483-014-1860-9

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A new first-order optimality condition for the basis pursuit denoise (BPDN) problem is derived. This condition provides a new approach to choose the penalty param- eters adaptively for a fixed point iteration algorithm. Meanwhile, the result is extended to matrix completion which is a new field on the heel of the compressed sensing. The numerical experiments of sparse vector recovery and low-rank matrix completion show validity of the theoretic results.