应用数学和力学

2008 Vol. 29, No. 5

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ZHU Li, LI Xiu-hua, GOU Xing-ming

2008, 29(5): 505-514.

Abstract(2823) PDF(706)

Abstract:
Some properties of the state operators of the optimal obstacle control problem for elliptic variational inequality was discussed,and the existence,uniqueness and regularity of the optimal control problem were established.In addition,the approximate problem of the optimal obstacle problem also was studied.

Algorithms of Common Solutions for Quasi Variational Inclusion and Fixed Point Problems

ZHANG Shi-sheng, LEE Joseph H W, CHAN Chi Kin

2008, 29(5): 515-524.

Abstract(2924) PDF(839)

Abstract:
The purpose is to present an iterative scheme for finding a common element of the set of solutions of the variational inclusion problem with multi-valued maximal monotone mapping and inverse-strongly monotone mappings and the set of fixed points of nonexpansive mappings in Hilbert space.Under suitable conditions,some strong convergence theorems for approximating to this common elements were proved.The results presented not only improve and extend the main results in Korpelevich[Ekonomika i Matematicheskie Metody,1976,12(4):747-756],but also extend and replenish the corresponding results in Iiduka and Takahashi[Nonlinear Anal,TMA,2005,61(3):341-350], Takahashi and Toyoda[J Optim Theory Appl,2003,118(2):417-428],Nadezhkina and Takahashi[J Optim Theory Appl,2006,128(1):191-201]and Zeng and Yao[Taiwanese Journal of Mathematics, 2006,10(5):1293-1303].

Terminal Sliding Mode Control for Coordinated Motion of Space Rigid Manipulator With External Disturbance

GUO Yi-shen, CHEN Li

2008, 29(5): 525-532.

Abstract(2808) PDF(625)

Abstract:
The control problem of coordinated motion of free-floating space rigid manipulator with external disturbance is discussed.With the relationship of the linear momentum conversation and the Lagrangian approach,the full-controlled dynamic equation and the Jacobian relation of free-floating space rigid manipulator were established and then inverted to the state equation for control design. Based on the terminal sliding mode control(SMC)technique,a mathematical expression of the terminal sliding surface was proposed,and then the terminal SMC scheme was developed for coordinated motion between the base's attitude and the end-effector of free-floating space manipulator with external disturbance.This proposed control scheme not only guarantees that the sliding phase of the closed-loop system exists,but also ensures that the output tracking error converges to zero in finite time.In addition,since the initial state of system is always at the terminal sliding surface,the control scheme can eliminate the reaching phase of the SMC and guarantee the global robustness and stability of the closed-loop system.A planar free-floating space rigid manipulator is simulated to verify the feasibility of the proposed control scheme.

Self-Adaptive Strategy for One-Dimensional Finite Element Method Based on EEP Method With Optimal Super-Convergence Order

YUAN Si, XING Qin-yan, WANG Xu, YE Kang-sheng

2008, 29(5): 533-543.

Abstract(3028) PDF(622)

Abstract:
Based on the newly-developed element energy projection(EEP)method with optimal super-convergence order for computation of super-convergent results,an improved self-adaptive strategy for one-dimensional finite element method(FEM)was proposed.In the strategy,a posteriori errors were estimated by comparing FEM solutions to EEP super-convergent solutions with optimal order of super-convergence,meshes were refined by using error-averaging method,and quasi -FEM solutions were used to replace true FEM solutions in the adaptive process.This strategy has been found to be simple,clear,efficient and reliable.For most of the problems,only one adaptive step is needed to produce the required FEM solutions which pointwise satisfy the user specified error tolerances in max-norm.Taking the elliptical ordinary differential equation of second order as the model problem,the fundamental idea,implementation strategy and computational algorithm were described and representative numerical examples were given to show the effectiveness and reliability of the proposed approach.

Aerodynamic Optimization of 3D Wing Based on iSIGHT

YIN Bo, XU Dian, AN Yi-ran, CHEN Yao-song

2008, 29(5): 544-550.

Abstract(3498) PDF(977)

Abstract:
A method of combining the CFD software,Fluent,with iSIGHT design platform was presented to optimize three-dimensional wing to ameliorate its aerodynamics performance.In the optimization design,two kinds of the genetic algorithm(GA),the NCGA(neighborhood cultivation GA) and the NSGA-Ⅱ(non-dominated sorting GA)were employed and the N-S equations were adopted to derive the aerodynamics functions of the 3D wing.The aerodynamic performance of the optimized wing has been significantly improved,which shows that the approach can be extended and employed in other cases.

Characteristic Finite Difference Method and Application for Moving Boundary Value Problem of the Coupled System

YUAN Yi-rang, LI Chang-feng, YANG Cheng-shun, HAN Yu-ji

2008, 29(5): 551-563.

Abstract(2958) PDF(587)

Abstract:
The coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of prospecting and exploiting oil-gas resources.The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values.A kind of characteristic finite difference schemes was put forward,from which optimal order estimates in norm was derived for the error in the approximate solutions.The research is important both theoretically and practically for the model analysis in the field,for model numerical method and for software development.

Moving Screw Dislocation Near Interfacial Rigid Lines in Two Dissimilar Anisotropic Media

LIU You-wen, LI Bo, FANG Qi-hong

2008, 29(5): 564-574.

Abstract(2432) PDF(661)

Abstract:
The problem for the interaction between a uniformly moving screw dislocation and interface rigid lines in two dissimilar anisotropic materials are investigated.Using Riemann-Schwarz's symmetry principle integrated with the analysis singularity of complex functions,the general elastic solutions of this problem and the closed form solutions for interface containing one and two rigid lines were presented.The expressions of stress intensity factors at the rigid line tips and image force acting on moving dislocation were derived explicitly.The results show that dislocation velocity has antishielding effect on rigid line tip and larger dislocation velocity leads to the equilibrium position of dislocation closing with rigid line.The presented solutions contain previously known results as the special cases.

Numerical Method for the Nonlinear Two-Phase Displacement Problem and Its Application

YUAN Yi-rang, LIANG Dong, RUI Hong-xing, DU Ning, WANG Wen-qia

2008, 29(5): 575-588.

Abstract(2701) PDF(629)

Abstract:
For the three-dimensional nonlinear two-phase displacement problem,the modified up-wind finite difference fractional steps schemes were put forward'some techniques,such as calculus of variations,induction hypothesis,decomposition of high order difference operators,the theory of prior estimates and techniques were used.Optimal order estimates were derived for the error in the approximation solution.These methods have been successfully used in predicting the consequences of seawater intrusion and protection projects.

Permanence and Global Attractivity of a Stage-Structured Predator-Prey Model With Continuous Harvesting on Predator and Impulsive Stocking on Prey

JIAO Jian-jun, CHEN Lan-sun, Juan J. Nieto, Torres Angela

2008, 29(5): 589-600.

Abstract(2320) PDF(536)

Abstract:
A stage-structured delayed predator-prey model with impulsive stocking on prey and continuous harvesting on predator is investigated.According to the fact of biological resource management,the assumption of a predator-prey model with stage structure for predator population that each individual predator has the same ability to capture prey was improved.It was assumed that the immature individuals and the mature individuals of the predator population were divided by a fixed age and that immature predator population does not have the ability to attack prey'sufficient conditions, which guarantee the global attractivity of predator-extinction periodic solution and the permanence of the system,were obtained.The results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system,and provides tactical basis for the biological resource management.Furthermore,numerical analysis is inserted to illuminate the dynamics of the system.

Alternative Principles and Minimax Inequalities in G-Convex Spaces

Mircea Balaj

2008, 29(5): 601-608.

Abstract(3020) PDF(639)

Abstract:
By using a fixed point theorem due to Kuo,Jeng and Huang in G-convex spaces a very general intersection theorem concerning the values of three maps was obtained.From this result successively alternative theorems concerning maximal elements,analytic alternatives and minimax inequalities were derived.

Computation of Compressible Flows With High Density Ratio and Pressure Ratio

CHEN Rong-san

2008, 29(5): 609-617.

Abstract(2644) PDF(636)

Abstract:
WENO method,RKDG method,RKDG method with original Ghost Fluid method and RKDG method with modified Ghost Fluid method were applied to single-medium and two-medium air-air,air-liquild compressible flow with high density and pressure ratios.Numerical comparison and analysis for the methods above were given.Numerical results show that,compared with the other methods,RKDG method with modified Ghost Fluid method can obtain high resolution and the correct position of the shock,the computed solutions are converge to physical solutions as the mesh refined.

Optimal Harvesting for an Age-Dependent n-Dimensional Food Chain Model

LUO Zhi-xue, DU Ming-yin

2008, 29(5): 618-630.

Abstract(2624) PDF(706)

Abstract:
Optimal harvesting policy for an age-dependent n-dimensional food chain model is studied.The existence and uniqueness of non-negative solution of the system were proved using the fixed point theorem.By Mazur's theorem,the existence of optimal control strategy was demonstrated and optimality conditions were derived by means of normal cone.