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HAMILTONIAN SYSTEM AND THE SAINT VENANT PROBLEM IN ELASTICITY

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Applied Mathematics and Mechanics(English Edition) 1996年第9期17卷 827-836页

作者：钟万勰徐新生张洪武 Research Institute of Engineering Mechanics Dalian University of Technology Dalian P. R. China

The traditional semi-inverse solution method of the Saint Venant problem, which is described in the Euclidian space under the Lagrangian system formulation, is updated to be solved in the symplectic space under the conservative hamiltonian system. It was proved in the present paper that all the Saint Venant solutions can be obtained directly via the zero eigenvalue solutions and all their Jordan normal form of the corresponding Hamiltonian operator matrix.

关键词： boundary value problems Elasticity Partial differential equations

SOME GENERAL THEOREMS AND GENERALIZED AND PIECEWISE GENERALIZED VARIATIONAL PRINCIPLES FOR LINEAR ELASTODYNAMICS

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Applied Mathematics and Mechanics(English Edition) 1992年第9期13卷 825-840页

作者：邢京堂郑兆昌 Peking Institute of Aeronautics and Astronautics Beijing Tsinghua University Beijing

From the concept of four-dimensional space and under the four kinds of time limit conditions, some general theorems for elastodynamics are developed, such as the principle of possible work action, the virtual displacement principle, the virtual stress-momentum principle, the reciprocal theorems and the related theorems of time terminal conditions derived from it. The variational principles of potential energy action and complementary energy action, the H-W principles, the H-R principles and the constitutive variational principles for elastodynamics are obtained. Hamilton's principle, Toupin's work and the formulations of Ref. [5], [17]-[24] may be regarded as some special cases of the general principles given in the paper. By considering three cases: piecewise space-time domain, piecewise space domain, piecewise time domain, the piecewise variational principles including the potential, the complementary and the mixed energy action fashions are given. Finally, the general formulation of piecewise variational principles is derived. If the time dimension is not considered, the formulations obtained in the paper will become the corresponding ones for elastostatics.

关键词： boundary value problems Dynamics Mathematical models Piecewise linear techniques Stresses Theory Time domain analysis Variational techniques

NUMERICAL SOLUTION OF SINGULAR PERTURBATION problems FOR THE FOURTH-ORDER ELLIPTIC DIFFERENTIAL EQUATIONS

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Applied Mathematics and Mechanics(English Edition) 1991年第10期12卷 943-966页

作者：苏煜城刘国庆 Nanjing University Nanjing Nanjing Institute of Chemical Technology Nanjing

In this paper we construct the finite-difference scheme for the singularly perturbed boundary value problem for the fourth-order elliptic differential equation on the basis of paper [1], and prove the uniform convergence of this scheme with respect to the small parameter Ε in the discrete energy norm. Finally, we give a numerical example.

关键词： Mathematical Techniques boundary value problems

NUMERICAL MODEL FOR COMPUTING WAVE LOADS ON ARBITRARY SHAPED STRUCTURES

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China Ocean Engineering 1989年第4期4卷 433-442页

作者： Zhang, Libang First Inst of Oceanography China

A Modified Hybrid Element Method (MHEM) for computing wave loads on arbitrary geometric bodies is presented in this paper. The additional unknowns in Mei's method are eradicated. Water depth varies in space. The MHEM adopts simple functionals to simplify the numerical scheme and the ICCG method to save CPU and storage; thus computing wave loads for a large flow domain or short waves can be carried out on small-sized computers or even microcomputers. Numerical results are compared with analytical solutions and experimental data. Good agreement is observed.

关键词： Computers, Microcomputer Mathematical Models Mathematical Techniques boundary value problems

PERIODIC SOLUTION TO A KIND OF SINGULARLY PERTURBED DIFFERENTIAL EQUATIONS OF PARABOLIC TYPE IN CHEMICAL KINETICS

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Applied Mathematics and Mechanics(English Edition) 1991年第5期12卷 461-468页

作者：倪明康 Department of Mathematics East China Normal University Shanghai

This paper deals with the problem on the periodic solution for the singularly perturbed differential equations of parabolic type originating from chemical kinetics stratified media. A uniformly valid asymptotic soluti... 详细信息

关键词： Mathematical Techniques boundary value problems Mathematical Techniques Differential Equations

WAVE DIFFRACTION BY A WEDGE OR CORNER WITH ARBITRARY REFLECTION PROPERTIES

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China Ocean Engineering 1990年第4期5卷 421-446页

作者： Hong, Guangwen Zhang, Yanqing Hohai Univ Nanjing China

In this paper a general analytical solution is presented for wave diffraction by a wedge or a corner of arbitrary angle (γ π, 0 0 and Rγ), in which, the cases of R0 = Rγ and Rγ = -R0 are included as special ones. The corresponding mathematical models for computation in engineering applications are derived. Numerical results and comparisons are also given.

关键词： Mathematical Models Mathematical Techniques boundary value problems

Solution of time-domain Maxwell equation with PML by using modified Laguerre polynomials

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Science in China(Series F) 2008年第5期51卷 550-559页

作者： LI LianLin LI Fang Institute of Electronics Chinese Academy of Sciences Beijing 100080 China

In this work, a stable numerical algorithm proposed by Chung et al. for the time-domain Maxwell equations is generalized. The time-domain Maxwell equations are solved by expressing the transient behaviors in terms of the modified Laguerre polynomials, and then the original equations of the initial value and boundary value can be transformed into a series of problems independent of the time variable. In this case the method of finite difference （FD）, the finite element method （FEM）, the method of moment （MoM）, etc. or the combination of these methods can be used to solve the problems. Finally, a numerical model is provided for the scattering problem with perfect matched layer （PML） by using FD. The comparison between the results of the proposed method and FDTD is presented to verify the proposed new method.

关键词： time-domain Maxwell equations modified Laguerre polynomials boundary value problems

TENSILE INSTABILITY OF NONLINEAR SPHERICAL MEMBRANE WITH LARGE DEFORMATION

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Applied Mathematics and Mechanics(English Edition) 1991年第10期12卷 993-1000页

作者：尚新春 Department of Mechanics Lanzhou University Lanzhou

The problem on instability on nonlinear spherical membrane with large axisymmetric tensile deformations is investigated by using the bifurcation theory. It is proved that all singular points of the nonlinear boundary value problem must be simple limit points. The effect of loading and material parameters on the equilibrium state and its stability is discussed.

关键词： Mathematical Techniques boundary value problems Mathematical Techniques Nonlinear Equations Membranes Stability

Long Waves Induced by Wave Groups over a Trench

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China Ocean Engineering 1991年第2期6卷 191-202页

作者： Zuo, Qihua Yao, Guoquan Nanjing Hydraulic Research Inst Nanjing China

The second order long waves of the mean water free surface displacement induced by the wave groups over a trench are discussed in this paper. The incident wave groups are supposed to be superposed by 2 linear waves with different amplitudes, phases and slightly different frequencies. Some of the theoretical formulas and numerical results are presented.

关键词： Mathematical Techniques boundary value problems