应用数学和力学

Modal Synthesis Method for Norm Computation of H_∞ Decentralized Control Systems (Ⅰ)

ZHONG Wan-xie, WU Zhi-gang, GAO Qiang, A. Y. T. Leung, F. W. Williams

2004, 25(2): 111-120.

Abstract(2579) PDF(1002)

Abstract:
When using H_∞ techniques to design decentralized controllers for large systems,the whole system is divided into subsystems,which are analysed using H_∞ control theory before being recombined.An analogy was established with substructural analysis in structural mechanics,in which H_∞ decentralized control theory corresponds to substructural modal synthesis theory so that the optimal H_∞ norm of the whole system corresponds to the fundamental vibration frequency of the whole structure.Hence,modal synthesis methodology and the extended Wittrick-Williams algorithm were transplanted from structural mechanics to compute the optimal H_∞ norm of the control system.The orthogonality and the expansion theorem of eigenfunctions of the subsystems H_∞ control are presented in part(Ⅰ) of the paper.The modal synthesis method for computation of the optimal H_∞ norm of decentralized control systems and numerical examples are presented in part(Ⅱ).

Modal Synthesis Method for Norm Computation of H_∞ Decentralized Control Systems (Ⅱ)

ZHONG Wan-xie, WU Zhi-gang, GAO Qiang, A. Y. T. Leung, F. W. Williams

2004, 25(2): 121-127.

Abstract(2291) PDF(605)

Abstract:
When using H_∞ techniques to design decentralized controllers for large systems,the whole system is divided into subsystems,which are analysed using H_∞ control theory before being recombined.An analogy was established with substructural analysis in structural mechanics,in which H_∞ decentralized control theory corresponds to substructural modal synthesis theory so that the optimal H_∞ norm of the whole system corresponds to the fundamental vibration frequency of the whole structure.Hence,modal synthesis methodology and the extended Wittrick-Williams algorithm were transplanted from structural mechanics to compute the optimal H_∞ norm of the control system.The orthogonality and the expansion theorem of eigenfunctions of the subsystems H_∞ control are presented in part(Ⅰ) of the paper.The modal synthesis method for computation of the optimal H_∞ norm of decentralized control systems and numerical examples are presented in part(Ⅱ).

Concepts of Mechanical Parameters Transfer in Solid Medium and Its Application in Engineerings

ZHAO Xiao-bing, XUE Da-wei, ZHAO Yu-xiang, ZHOU Feng-jun

2004, 25(2): 128-134.

Abstract(2040) PDF(504)

Abstract:
Based on investigation into four aspects of qualitative mechanical analysis,principle model experiments,engineering dynamic load tests and numerical calculation,it was discussed that the transfer of stresses and accelerations in stratum medium have a close relation with its relative rigidity. The concepts of stresses and accelerations transfer in solid medium and its corresponding generalized, composite structure system are presented.The survivability of underground engineerings and protective engineering will be greatly increased if these concepts are correctly used in construction.

Boundary Element Analysis of Interaction Between an Elastic Rectangular Inclusion and a Crack

WANG Yin-bang

2004, 25(2): 135-140.

Abstract(2660) PDF(510)

Abstract:
The interaction between an elastic rectangular inclusion and a kinked crack in an infinite elastic body was considered by using boundary element method.The new complex boundary integral equations were derived.By introducing a complex unknown function H(t)related to the interface displacement density and traction and applying integration by parts,the traction continuous condition was satisfied automatically.Only one complex boundary integral equation was obtained on interface and involves only singularity of order 1/r.To verify the validity and effectiveness of the present boundary element method,some typical examples were calculated.The obtained results show that the crack stress intensity factors decrease as the shear modulus of inclusion increases.Thus,the crack propagation is easier near a softer inclusion and the harder inclusion is helpful for crack arrest.

Influences of the Fish-Mouth Project and the Groins on the Flow and Sediment Ratio of the Yangtze River Waterway

ZHOU Ji-fu, LI Jia-chun

2004, 25(2): 141-149.

Abstract(2422) PDF(548)

Abstract:
A depth-integrated two-dimensional numerical model of current,salinity and sediment transport was proposed and calibrated by the observation data in the Yangtze River Estuary.It was then applied to investigate the flow and sediment ratio of the navigation channel,i.e.the North Channel of the Yangtze River Estuary,before and after the first phase waterway project is implemented. Particularly,the influences of groin length and the orientation of the submerged dam on the flow ratio and sediment load discharging into the North Channel were discussed.The numerical results demonstrate that less sediment load discharges into the navigation channel,which unburdens the waterway dredging,but in the meantime the flow ratio is also decreased.The flow and sediment ratio can be adjusted by changing layout and dimensions of the hydro-structures,such as the groin length,the top height,etc.The effect of the orientation of the submerged dam is more obvious than the groin lengh.

On the Periodic Solutions of Differential Inclusions and Applications

LI Guo-cheng, XUE Xiao-ping, SONG Shi-ji

2004, 25(2): 150-158.

Abstract(2773) PDF(593)

Abstract:
The periodic problem of evolution inclusion is studied and its results are used to establish existence theorems of periodic solutions of a class of semi-linear differential inclusion.Also existence theorem of the extreme solutions and the strong relaxation theorem are given for this class of semi-linear differential inclusion.An application to some feedback control systems is discussed.

Symplectic Solution System for Reissner Plate Bending

YAO Wei-an, SUI Yong-feng

2004, 25(2): 159-165.

Abstract(2603) PDF(1043)

Abstract:
Based on the Hellinger-Reissner variatonal principle for Reissner plate bending and introducing dual variables,Hamiltonian dual equations for Reissner plate bending were presented.Therefore Hamiltonian solution system can also be applied to Reissner plate bending problem,and the transformation from Euclidian space to symplectic space and from Lagrangian system to Hamilt onian system was realized.So in the symplectic space which consists of the original variables and their dual variables,the problem can be solved via effective mathematical physics methods such as the method of separation of variables and eigenfunction-vector expansion.All the eigensolutions and Jordan canonical form eigensolutions for zero eigenvalue of the Hamiltonian operator matrix are solved in detail,and their physical meanings are showed clearly.The adjoint symplectic orthonormal relation of the eigen-function vectors for zero eignevalue are formed.It is showed that the all eigensolutions for zero eigen-value are basic solutions of the Saint-Venant problem and they form a perfect symplectic subspace for zero eigenvalue.And the eigensolutions for nonzero eigenvalue are covered by the Saint-Venant theorem.The symplectic solution method is not the same as the classical semi-inverse method and breaks through the limit of the traditional semi-inverse solution.The symplectic solution method will have vast application.

Mixed Finite Element Methods for the Shallow Water Equations Including Current and Silt Sedimentation (Ⅱ)-The Discrete-Time Case Along Characteristics

LUO Zhen-dong, ZHU Jiang, ZENG Qing-cun, XIE Zheng-hui

2004, 25(2): 166-180.

Abstract(2663) PDF(501)

Abstract:
The mixed finite element(MFE)methods for a shallow water equation system consisting of water dynamics equations,silt transport equation,and the equation of bottom topography change were derived.A fully discrete MFE scheme for the discrete-time along characteristics is presented and error estimates are established.The existence and convergence of MFE solution of the discrete current velocity,elevation of the bottom topography,thickness of fluid column,and mass rate of sediment is demonstrated.

Modified Integral-Level Set Method for the Constrained Solving Global Optimization

TIAN Wei-wen, WU Dong-hua, ZHANG Lian-sheng, LI Shan-liang

2004, 25(2): 181-188.

Abstract(2572) PDF(680)

Abstract:
The constrained global optimization problem being considered,a modified integral-level set method was illustrated based on Chew-Zheng's paper on Integral Global Optimization and Wu's paper on Implementable Algorithm Convergence of Modified Integral-Level Set Method for Global Optimization Poblem.It has two characters:1)each phase must construct a new function which has the same global optimal value as that of primitive objective function;2)comparing it with Zheng's method, solving level set procedure is avoided.An implementable algorithm also is given and it is proved that this algorithm is convergent.

Local Petrov-Galerkin Method for a Thin Plate

XIONG Yuan-bo, LONG Shu-yao

2004, 25(2): 189-196.

Abstract(2974) PDF(664)

Abstract:
The meshless local Petrov-Galerkin(MLPG)method for solving the bending problem of the thin plate were presented and discussed.The method used the moving least-squares approximation to interpolate the solution variables,and employed a local symmetric weak form.The present method was a truly meshless one as it did not need a finite element or boundary element mesh,either for purpose of interpolation of the solution,or for the integration of the energy.All integrals could be easily evaluated over regularly shaped domains(in general,spheres in three-dimensional problems)and their boundaries.The essential boundary conditions were enforced by the penalty method.Several numerical examples were presented to illustrate the implementation and performance of the present method.The numerical examples presented show that high accuracy can be achieved for arbitrary grid geometries for clamped and simply-supported edge conditions.No post processing procedure is required to computer the strain and stress,since the original solution from the present method,using the moving least squares approximation,is already smooth enough.

Hybrid Perturbation-Galerkin Solution of the Flow in a Circular Cross-Section Tube With Constriction

SHEN Xin-rong, GAO Qi, ZHANG Ben-zhao, ZHANG Jin-suo

2004, 25(2): 197-205.

Abstract(2405) PDF(584)

Abstract:
Using hybrid perturbatin-Galerkin technique,a crcular cross-section tube model with sinu-soidal wall is studied.This technique can remove the limitation of small parameters for perturbation and the difficulty of selecting good coordinate functions about Galerkin technique.The effects caused by the boundary conditions and the Reynolds number on the flow were discussed.The position of the separate and reattachment points was obtained.The tendency of the variation about the shear stress on the wall and friction factor along the axis direction were also analyzed.The results at a small parameter have good agreements with the perturbation ones.

Asymptotic Analysis of Mode Ⅱ Stationary Growth Crack on Elastic-Elastic Power Law Creeping Bimaterial Interface

TANG Li-qiang, LI Yong-dong, LIU Chang-hai

2004, 25(2): 206-212.

Abstract(2487) PDF(1203)

Abstract:
A mechanical model was established for mode Ⅱ interfacial crack static growing along an elastic-elastic power law creeping bimaterial interface.For two kinds of boundary conditions on crack faces,traction free and frictional contact,asymptotic solutions of the stress and strain near tip-crack were given.Results deriv ed indicate that the stress and strain have the same singularity,there is not the oscillatory singularity in the field;the creep power-har dening index n and the ratio of Young's module notably influence the crack-tip field in region of elastic power law creeping material and nonly influence distribution of stresses and strains in region of elastic material.When n is bigger,the creeping deformation is dominant and stress fields become steady,which does not change with n. Poisson's ratio does not affect the distributing of the crack-tip field.

Class of Alternating Group Method of Burgers’ Equation

WANG Wen-qia

2004, 25(2): 213-220.

Abstract(2721) PDF(648)

Abstract:
Some new Saul'yev type asymmetric difference schemes for Burgers'equation is given,by the use of the schemes,a kind of alternating group four points method for solving nonlinear Burgers' equation is constructed here.The basic idea of the method is that the grid points on the same time level is divided into a number of groups,the difference equations of each group can be solved independently,hence the method with intrinsic parallelism can be used directly on parallel computer.The method is unconditionally stable by analysis of linearization procedure.The numerical experiments show that the method has good stability and accuracy.

2004 Vol. 25, No. 2