应用数学和力学

2012 Vol. 33, No. 2

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Transition Sets of Bifurcations of Dynamical System With Two State Variables With Constraints

LI Jun, CHEN Yu-shu

2012, 33(2): 135-152. doi: 10.3879/j.issn.1000-0887.2012.02.001

Abstract(1998) PDF(785)

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

Finite-Time Stabilization of Uncertain Non-Autonomous Chaotic Gyroscopes With Nonlinear Inputs

Mohammad Pourmahmood Aghababa, Hasan Pourmahmood Aghababa

2012, 33(2): 153-163. doi: 10.3879/j.issn.1000-0887.2012.02.002

Abstract(1939) PDF(797)

Abstract:
Gyroscopes were one of the most interesting and everlasting onlinear non-autonomous dynamical systems that exhibited very complex dynamical behavior such as chaos. The problem of robust stabilization of the nonlinear non-autonomous gyroscopes in a given finite time was studied. It was assumed that the gyroscope system was perturbed by model uncertainties, external disturbances and unknown parameters. Besides, the effects of input nonlinearities were taken into account. Appropriate adaptive laws were proposed to tackle the unknown parameters. Based on the adaptive laws and the finite-time control theory, discontinuous finite-time control laws were 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.

Effects of Renal Artery Stenosis in a Realistic Model of Abdominal Aorta and Renal Arteries Incorporating FSI and Pulsatile Non-Newtonian Blood Flow

Zahra Mortazavinia, Amin Zare, Alireza Mehdizadeh

2012, 33(2): 164-176. doi: 10.3879/j.issn.1000-0887.2012.02.003

Abstract(1469) PDF(699)

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

Modified Characteristic Finite Difference Fractional Steps Method for Moving Boundary Value Problem of Percolation Coupled System

YUAN Yi-rang, LI Chang-feng, SUN Tong-jun

2012, 33(2): 177-194. doi: 10.3879/j.issn.1000-0887.2012.02.004

Abstract(1962) PDF(825)

Abstract:
For coupled system with moving boundary values of multilayer dynamics of fluids in porous media,a kind of characteristic finite difference fractional steps scheme applicable to parallel arithmetic were put forward. Some techniques, such as the change of regions, calculus of variations, piecewise threefold quadratic interpolation, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates, were adopted. Optimal order estimates in l²norm are derived to determine the error in the approximate solution. This method has already been applied to the numerical simulation of migrationaccumulation of oil resources.

Numerical Investigation of the Dufour and Soret Effects on Unsteady MHD Natural Convection Flow Past a Vertical Plate Embedded in a Non-Darcy Porous Medium

Mohammed Q Al-Odat, Abdalmajeed Al-Ghamdi

2012, 33(2): 195-209. doi: 10.3879/j.issn.1000-0887.2012.02.005

Abstract(1633) PDF(737)

Abstract:
The Dufour and Soret effects on 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 were investigated numerically. The governing non-linear dimensionless equations were solved using an implicit finite difference scheme of Crank-Nicolson type with a tri-diagonal matrix manipulation. The effects of various parameters entering into the problem on the unsteady dimensionless velocity, temperature and concentration profiles were studied in detail. Furthermore, the time variation of the skin friction coefficient, the Nusselt number and the Sherwood number were presented and analyzed. The results of the present investigation show that the unsteady velocity, temperature and concentration profiles are substantially influenced by the Dufour and Soret effects. As 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 temperature decrease in the boundary layer.

Monolithic Approach to Thermal Fluid Structure Interaction With Non-Conforming Interfaces

YIN Liang, JIANG Jun-cheng, ZHANG Li-xiang

2012, 33(2): 210-220. doi: 10.3879/j.issn.1000-0887.2012.02.006

Abstract(1947) PDF(821)

Abstract:
A monolithic approach to thermal fluid structure interaction with non-conforming interfaces was presented. The thermal viscous flow was governed by the Boussinesq approximation and the incompressible Navier-Stokes equations.The motion of the fluid domain was accounted for by an arbitrary Lagrangian-Eulerian (ALE) strategy. A pseudo-solid formulation was used to manage the deformation of the fluid domain. The structure was described by geometrically nonlinear thermoelastic dynamics. An efficient data transfer strategy based on Gauss points was proposed to guarantee equilibrium of the stresses and heat along the interface. The resulting strongly coupled set of non-linear equations for fluid, structure, heat was solved by a monolithic solution procedure. Numerical example was 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): 221-230. doi: 10.3879/j.issn.1000-0887.2012.02.007

Abstract(1708) PDF(789)

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

On a Class of Metal-Forming Problems With Combined Hardening

T.A.Angelov

2012, 33(2): 231-239. doi: 10.3879/j.issn.1000-0887.2012.02.008

Abstract(1632) PDF(732)

Abstract:
A class of quasi-steady metalforming problems, with incompressible, rigidplastic, strain-rate dependent, isotropic and kinematic hardening material model and with nonlocal contact and Coulomb’s friction boundary conditions was considered. A coupled variational formulation was derived and by proving the convergence of a variable stiffness parameters method with time retardation, existence and uniqueness results were obtained.

Anisotropic Nonconforming Crouzeix-Raviart Type FEM for Second Order Elliptic Problems

SHI Dong-yang, XU Chao

2012, 33(2): 240-249. doi: 10.3879/j.issn.1000-0887.2012.02.009

Abstract(2140) PDF(760)

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

A New Exact Penalty Function for Solving Constrained Finite Min-Max Problems

MA Cheng, LI Xun, YIU Ka-Fai Cedric, ZHANG Lian-sheng

2012, 33(2): 250-264. doi: 10.3879/j.issn.1000-0887.2012.02.010

Abstract(1718) PDF(855)

Abstract:
A new exact yet smooth penalty function to tackle constrained min-max problems was introduced. Using this new penalty function and adding just one extra variable, a constrained min-max problem was transformed into an unconstrained optimization one. It was proved that, under certain reasonable assumptions and when the penalty parameter was sufficiently large, the minimizer of this unconstrained optimization problem was equivalent to the minimizer of the original constrained one. Moreover, the local exactness property was also studied. The numerical results demonstrate that this penalty function method is an effective and promising approach for solving constrained finite min-max problems.