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2012年 第33卷 第2期    刊出日期：2012-01-11

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Articles

Transition sets of bifurcations of dynamical systems with two state variables with constraints

李军 陈予恕

2012, 33(2):  139-154.  doi:10.1007/s10483-012-1539-7

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Bifurcation of periodic solutions widely exists in nonlinear dynamical systems. In this paper, categories of bifurcations of systems with two state variables with different types of constraints are discussed, where some new types of transition sets are added. Additionally, the bifurcation properties of two-dimensional systems without constraints are compared with the ones with constraints. The results obtained in this paper can be used by engineers for the choice of the structural parameters of the systems.

论文

Finite-time stabilization of uncertain non-autonomous chaotic gyroscopes with nonlinear inputs

M. P. AGHABABA H. P. AGHABABA

2012, 33(2):  155-164.  doi:10.1007/s10483-012-1540-7

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Gyroscopes are one of the most interesting and everlasting nonlinear nonautonomous dynamical systems that exhibit very complex dynamical behavior such as chaos. In this paper, the problem of robust stabilization of the nonlinear non-autonomous gyroscopes in a given finite time is studied. It is assumed that the gyroscope system is perturbed by model uncertainties, external disturbances, and unknown parameters. Besides, the effects of input nonlinearities are taken into account. Appropriate adaptive laws are proposed to tackle the unknown parameters. Based on the adaptive laws and the finite-time control theory, discontinuous finite-time control laws are proposed to ensure the finite-time stability of the system. The finite-time stability and convergence of the closed-loop system are analytically proved. Some numerical simulations are presented to show the efficiency of the proposed finite-time control scheme and to validate the theoretical results.

Articles

Effects of renal artery stenosis on realistic model of abdominal aorta and renal arteries incorporating fluid-structure interaction and pulsatile non-Newtonian blood flow

Z. MORTAZAVINIA A.ZARE A. MEHDIZADEH

2012, 33(2):  165-176.  doi:10.1007/s10483-012-1541-6

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The effects of the renal artery stenosis (RAS) on the blood flow and vessel walls are investigated. The pulsatile blood flow through an anatomically realistic model of the abdominal aorta and renal arteries reconstructed from CT-scan images is simulated, which incorporates the fluid-structure interaction (FSI). In addition to the investigation of the RAS effects on the wall shear stress and the displacement of the vessel wall, it is determined that the RAS leads to decrease in the renal mass flow. This may cause the activation of the renin-angiotension system and results in severe hypertension.

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

袁益让 李长峰 孙同军

2012, 33(2):  177-194.  doi:10.1007/s10483-012-1542-x

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For the coupled system with moving boundary values of multilayer dynamics of fluids in porous media, a characteristic finite difference fractional step scheme applicable to the parallel arithmetic is put forward. Some techniques, such as the change of regions, the calculus of variations, the piecewise threefold quadratic interpolation, the multiplicative commutation rule of difference operators, the decomposition of high order difference operators, and the prior estimates, are adopted. The optimal order estimates in the l2 norm are derived to determine the error in the approximate solution. This numerical method has been successfully used to simulate the flow of migration-accumulation of the multilayer percolation coupled system. Some numerical results are well illustrated in this paper.

Numerical investigation of Dufour and Soret effects on unsteady MHD natural convection flow past vertical plate embedded in non-Darcy porous medium

M. Q. AL-ODAT A. AL-GHAMDI

2012, 33(2):  195-210.  doi:10.1007/s10483-012-1543-9

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The Dufour and Soret effects on the unsteady two-dimensional magnetohydrodynamics (MHD) double-diffusive free convective flow of an electrically conducting fluid past a vertical plate embedded in a non-Darcy porous medium are investigated numerically. The governing non-linear dimensionless equations are solved by an implicit finite difference scheme of the Crank-Nicolson type with a tridiagonal matrix manipulation. The effects of various parameters entering into the problem on the unsteady dimensionless velocity, temperature, and concentration profiles are studied in detail. Furthermore, the time variation of the skin friction coefficient, the Nusselt number, and the Sherwood number is presented and analyzed. The results show that the unsteady velocity, temperature, and concentration profiles are substantially influenced by the Dufour and Soret effects. When the Dufour number increases or the Soret number decreases, both the skin friction and the Sherwood number decrease, while the Nusselt number increases. It is found that, when the magnetic parameter increases, the velocity and the temperature decrease in the boundary layer.

Monolithic approach to thermal fluid-structure interaction with onconforming interfaces

殷亮 蒋成军 张立翔

2012, 33(2):  211-222.  doi:10.1007/s10483-012-1544-x

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This paper presents a monolithic approach to the thermal fluid-structure interaction (FSI) with nonconforming interfaces. The thermal viscous flow is governed by the Boussinesq approximation and the incompressible Navier-Stokes equations. The motion of the fluid domain is accounted for by an arbitrary Lagrangian-Eulerian (ALE) strategy. A pseudo-solid formulation is used to manage the deformation of the fluid domain. The structure is described by the geometrically nonlinear thermoelastic dynamics. An efficient data transfer strategy based on the Gauss points is proposed to guarantee the equilibrium of the stresses and heat along the interface. The resulting strongly coupled set of nonlinear equations for the fluid, structure, and heat is solved by a monolithic solution procedure. A numerical example is presented to demonstrate the robustness and efficiency of the methodology.

Eigenfunction expansion method of upper triangular operator matrix and application to two-dimensional elasticity problems based on stress formulation

EBURILITU ALATANCANG

2012, 33(2):  223-232.  doi:10.1007/s10483-012-1545-9

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This paper studies the eigenfunction expansion method to solve the twodimensional (2D) elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper triangular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler complete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and convenient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.

Metal-forming problems with combined hardening

T. A. ANGELOV

2012, 33(2):  233-242.  doi:10.1007/s10483-012-1546-8

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A class of quasi-steady metal-forming problems under nonlocal contact and Coulomb’s friction boundary conditions is considered with an incompressible, rigidplastic, strain-rate dependent, isotropic, and kinematic hardening material model. A coupled variational formulation is derived, the convergence of a variable stiffness parameter method with time retardation is proved, and the existence and uniqueness results are obtained.

Anisotropic nonconforming Crouzeix-Raviart type FEM for second-order elliptic problems

石东洋 许超

2012, 33(2):  243-252.  doi:10.1007/s10483-012-1547-8

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The nonconforming Crouzeix-Raviart type linear triangular finite element approximate to second-order elliptic problems is studied on anisotropic general triangular meshes in 2D satisfying the maximal angle condition and the coordinate system condition. The optimal-order error estimates of the broken energy norm and L2-norm are obtained.

New exact penalty function for solving constrained finite min-max problems

马骋 李讯 姚家辉 张连生

2012, 33(2):  253-270.  doi:10.1007/s10483-012-1548-6

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This paper introduces a new exact and smooth penalty function to tackle constrained min-max problems. By using this new penalty function and adding just one extra variable, a constrained min-max problem is transformed into an unconstrained optimization one. It is proved that, under certain reasonable assumptions and when the penalty parameter is sufficiently large, the minimizer of this unconstrained optimization problem is equivalent to the minimizer of the original constrained one. Numerical results demonstrate that this penalty function method is an effective and promising approach for solving constrained finite min-max problems.