当期目录

2013年 第34卷 第4期    刊出日期：2013-04-03

上一期    下一期

Analytical solution of rectangular plate with in-plane variable stiffness

于天崇 聂国隽 仲政 褚福运

2013, 34(4):  395-404.  doi:10.1007/s10483-013-1679-x

摘要 ( 756 )   PDF (231KB) ( 1028 )  

相关文章 | 多维度评价

The bending problem of a thin rectangular plate with in-plane variable stiffness is studied. The basic equation is formulated for the two-opposite-edge simply supported rectangular plate under the distributed loads. The formulation is based on the assumption that the flexural rigidity of the plate varies in the plane following a power form, and Poisson’s ratio is constant. A fourth-order partial differential equation with variable coefficients is derived by assuming a Levy-type form for the transverse displacement. The governing equation can be transformed into a Whittaker equation, and an analytical solution is obtained for a thin rectangular plate subjected to the distributed loads. The validity of the present solution is shown by comparing the present results with those of the classical solution. The influence of in-plane variable stiffness on the deflection and bending moment is studied by numerical examples. The analytical solution presented here is useful in the design of rectangular plates with in-plane variable stiffness.

Mathematical osteon model for examining poroelastic behaviors

武晓刚 陈维毅 王旦霞

2013, 34(4):  405-416.  doi:10.1007/s10483-013-1680-x

摘要 ( 763 )   PDF (726KB) ( 697 )  

相关文章 | 多维度评价

An extended and reasonable stress boundary condition at an osteon exterior wall is presented to solve the model proposed by R´emond and Naili. The obtained pressure and fluid velocity solutions are used to investigate the osteonal poroelastic behaviors. The following results are obtained. (i) Both the fluid pressure and the velocity amplitudes are proportional to the strain amplitude and the loading frequency. (ii) In the physiological loading state, the key role governing the poroelastic behaviors of the osteon is the strain rate. (iii) At the osteon scale, the pressure is strongly affected by the
permeability variations, whereas the fluid velocity is not.

Modified characteristic finite difference fractional step method for moving boundary value problem of nonlinear percolation system

袁益让 李长峰 孙同军 刘允欣

2013, 34(4):  417-436.  doi:10.1007/s10483-013-1681-8

摘要 ( 687 )   PDF (325KB) ( 536 )  

相关文章 | 多维度评价

A fractional step scheme with modified characteristic finite differences running in a parallel arithmetic is presented to simulate a nonlinear percolation system of multilayer dynamics of fluids in a porous medium with moving boundary values. With the help of theoretical techniques including the change of regions, piecewise threefold quadratic interpolation, calculus of variations, multiplicative commutation rule of difference operators, multiplicative commutation rule of difference operators, decomposition of high order difference operators, induction hypothesis, and prior estimates, an optimal order in l² norm is displayed to complete the convergence analysis of the numerical algorithm. Some numerical results arising in the actual simulation of migration-accumulation of oil resources by this method are listed in the last section.

论文

Free vibration and critical speed of moderately thick rotating laminated composite conical shell using generalized differential quadrature method

K. DANESHJOU M. TALEBITOOTI R. TALEBITOOTI

2013, 34(4):  437-456.  doi:10.1007/s10483-013-1682-8

摘要 ( 931 )   PDF (10693KB) ( 1113 )  

相关文章 | 多维度评价

The generalized differential quadrature method (GDQM) is employed to consider the free vibration and critical speed of moderately thick rotating laminated composite conical shells with different boundary conditions developed from the first-order shear deformation theory (FSDT). The equations of motion are obtained applying Hamilton’s concept, which contain the influence of the centrifugal force, the Coriolis acceleration,
and the preliminary hoop stress. In addition, the axial load is applied to the conical shell as a ratio of the global critical buckling load. The governing partial differential equations are given in the expressions of five components of displacement related to the points lying on the reference surface of the shell. Afterward, the governing differential equations are converted into a group of algebraic equations by using the GDQM. The outcomes
are achieved considering the effects of stacking sequences, thickness of the shell, rotating velocities, half-vertex cone angle, and boundary conditions. Furthermore, the outcomes indicate that the rate of the convergence of frequencies is swift, and the numerical technique is superior stable. Three comparisons between the selected outcomes and those of other research are accomplished, and excellent agreement is achieved.

Unified elastoplastic finite difference and its application

马宗源 廖红建 党发宁

2013, 34(4):  457-474.  doi:10.1007/s10483-013-1683-7

摘要 ( 841 )   PDF (1242KB) ( 1387 )  

相关文章 | 多维度评价

Two elastoplastic constitutive models based on the unified strength theory (UST) are established and implemented in an explicit finite difference code, fast Lagrangian analysis of continua (FLAC/FLAC3D), which includes an associated/nonassociated flow rule, strain-hardening/softening, and solutions of singularities. Those two constitutive models are appropriate for metallic and strength-different (SD) materials, respectively. Two verification examples are used to compare the computation results and test data using the two-dimensional finite difference code FLAC and the finite element code ANSYS, and the two constitutive models proposed in this paper are verified. Two application examples, the large deformation of a prismatic bar and the strain-softening behavior of soft rock under a complex stress state, are analyzed using the three-dimensional code FLAC3D. The two new elastoplastic constitutive models proposed in this paper can be used in bearing capacity evaluation or stability analysis of structures built of metallic or SD materials. The effect of the intermediate principal stress on metallic or SD material structures under complex stress states, including large deformation, three-dimensional and non-association problems, can be analyzed easily using the two constitutive models proposed in this paper.

Bifurcation of multi-freedom gear system with spalling defect

马锐 陈予恕

2013, 34(4):  475-488.  doi:10.1007/s10483-013-1684-7

摘要 ( 763 )   PDF (699KB) ( 611 )  

相关文章 | 多维度评价

This study focuses on the bifurcation characteristics of the four degree-offreedom gear system with local spalling defect to explore the spalling nonlinear dynamic mechanism. The dynamic model of the gear system with spalling defect, time-variant mesh stiffness, and nonlinear clearance is established to investigate the effect of spalling defect on mesh stiffness and dynamic bifurcation. The primary resonance and internal resonance responses of the spalling model are analyzed by the averaging method, and the bifurcation characteristics with the evolvement of spall and internal excitation are studied by employing the singularity theory for the two-state variable system, which reveal the different bifurcation characteristics caused by the spalling defect. The results obtained herein can provide a theoretical basis to spalling fault diagnosis of gearbox.

论文

Three-dimensional flow of Oldroyd-B fluid over surface with convective boundary conditions

T. HAYAT S. A. SHEHZAD A. ALSAEDI M. S. ALHOTHUALI

2013, 34(4):  489-500.  doi:10.1007/s10483-013-1685-9

摘要 ( 888 )   PDF (286KB) ( 1417 )  

相关文章 | 多维度评价

The present study addresses the three-dimensional flow of an Oldroyd-B fluid over a stretching surface with convective boundary conditions. The problem formulation is presented using the conservation laws of mass, momentum, and energy. The solutions to the dimensionless problems are computed. The convergence of series solutions by the homotopy analysis method (HAM) is discussed graphically and numerically. The graphs
are plotted for various parameters of the temperature profile. The series solutions are verified by providing a comparison in a limiting case. The numerical values of the local Nusselt number are analyzed.

Numerical and analytical investigations of thermosolutal instability in rotating Rivlin-Ericksen fluid in porous medium with Hall current

S. KUMAR V. SHARMA K. KISHOR

2013, 34(4):  501-522.  doi:10.1007/s10483-013-1686-6

摘要 ( 843 )   PDF (346KB) ( 581 )  

相关文章 | 多维度评价

Numerical and analytical investigations of the thermosolutal instability in a viscoelastic Rivlin-Ericksen fluid are carried out in the presence of a uniform vertical magnetic field to include the Hall current with a uniform angular velocity in a porous medium. For stationary convection, the stable solute gradient parameter and the rotation have stabilizing effects on the system, whereas the magnetic field and the medium permeability have stabilizing or destabilizing effects on the system under certain conditions. The Hall current in the presence of rotation has stabilizing effects for sufficiently large Taylor numbers, whereas in the absence of rotation, the Hall current always has destabilizing effects. These effects have also been shown graphically. The viscoelastic effects disappear for stationary convection. The stable solute parameter, the rotation, the medium permeability, the magnetic field parameter, the Hall current, and the viscoelasticity introduce oscillatory modes into the system, which are non-existent in their
absence. The sufficient conditions for the non-existence of overstability are also obtained.

Solitary wave solution to Aw-Rascle viscous model of traffic flow

吴春秀 张鹏 S. C. WONG 乔殿梁 戴世强

2013, 34(4):  523-528.  doi:10.1007/s10483-013-1687-9

摘要 ( 751 )   PDF (197KB) ( 636 )  

相关文章 | 多维度评价

A traveling wave solution to the Aw-Rascle traffic flow model that includes the relaxation and diffusion terms is investigated. The model can be approximated by the well-known Kortweg-de Vries (KdV) equation. A numerical simulation is conducted by the first-order accurate Lax-Friedrichs scheme, which is known for its ability to capture the entropy solution to hyperbolic conservation laws. Periodic boundary conditions are applied to simulate a lengthy propagation, where the profile of the derived KdV solution is taken as the initial condition to observe the change of the profile. The simulation shows good agreement between the approximated KdV solution and the numerical solution.