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THERMAL-BUCKLING OF THIN ANNULAR PLATES UNDER MULTIPLE LOADS

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Applied Mathematics and Mechanics(English Edition) 1991年第3期12卷 301-308页

作者：李世荣程昌钧 University of Gansu Technology Lanzhou Lanzhou University Lanzhou

On the basis of Von Karman equations, the thermal-buckling of thin annular plates subjected to a field of non-uniform axisymmetric temperature and a variety of boundary conditions is discussed. The linearized problem is analyzed and stability boundaries which characterize instability of a plate are obtained by means of numerical and analysis methods.

关键词： Mathematical Models Mathematical Techniques boundary value problems Thermal Effects

ASYMPTOTIC SOLUTIONS OF THE NONLINEAR STABILITY OF A TRUNCATED SHALLOW SPHERICAL SHELL UNDER A CONCENTRATED LOAD

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Applied Mathematics and Mechanics(English Edition) 1991年第3期12卷 313-326页

作者：康盛亮 Tongji University Shanghai

In this paper, the nonlinear stability problem of a clamped truncated shallow spherical shell with a nondeformable rigid body at the center under a concentrated load is studied by means of the singular perturbation me... 详细信息

关键词： Mathematical Models Mathematical Techniques boundary value problems Strength of Materials

ANALYTICAL SOLUTIONS OF THE HELICAL FLOW OF NONNEWTONIAN FLUID IN ECCENTRIC ANNULAR SPACE

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Applied Mathematics and Mechanics(English Edition) 1994年第7期15卷 657-670页

作者：张海桥吴继周 The Department of Basic Courses Daging Petroleum Institute Heilongjiang

Many problems in petroleum and chemical industry can be reduced to the solution of the helical flow of non-Newtonian fluid in eccentric annular space. The laminar helical flows of the power law fluid and Bingham fluid in eccentric annular space were studied. An approximate analytical solution was obtained by the infinite subdivision method, namely, the eccentric flow was replaced by the infinite concentric flows. Then, the expressions for apparent viscosity distribution, velocity distribution and the flow rate were derived for the power law fluid and the Bingham fluid respectively. In addition, the expressions for pressure drop and stability parameter were also given. It is concluded that this method is much easier to use and more accurate than the method which solves the equations directly. The results are useful for the drilling technology of oil industry, etc.

关键词： boundary value problems Confined flow Differential equations Laminar flow Non Newtonian liquids

NONLINEAR BENDING OF SHALLOW SPHERICAL SHELLS ON THE PASTERNAK FOUNDATIONS

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Applied Mathematics and Mechanics(English Edition) 1991年第5期12卷 455-460页

作者：林家骥惠兴中曹爱群 Xi'an Institute of Metallurgy and Construction and Engineering. Xi'an

Based on Karman's nonlinear fundamental differential equations, the new approach, which combines modified iteration method with Galerkin's one, has been put forward to solve nonlinear bending of shallow spherical shell with concave base and clamped edges on the Pasternak foundation under uniform loads in this paper. Mathematical expression of load-deflection has been given; furthermore, results obtained are in good agreement with existent ones.

关键词： Mathematical Techniques boundary value problems Mathematical Techniques Iterative Methods Strain Analysis Stresses Analysis

PLANE ELASTIC problems OF DIFFERENT MEDIA WITH CRACKS ON THE INTERFACE

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Applied Mathematics(A Journal of Chinese Universities) 1993年第1期8卷 15-24页

作者：路见可 Department of Mathematics Wuhan University Wuhan 430072

The equilibrium problem for the infinite elastic plane consisting of two different media with many cracks on the interface is discussed. It is transferred to a boundary value problem for analytic functions and then further reduced to a singular integral equation, the unique solvability and an effective method of solution for which are established. A practical example in applications is illustrated, the solution of which is obtained in closed form.

关键词： Cracks boundary value problems Singular Integral Equations.

Existence of Positive Solutions for Systems of Second-order Nonlinear Singular Differential Equations with Integral boundary Conditions on Infinite Interval

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Chinese Quarterly Journal of Mathematics 2014年第1期29卷 55-64页

作者： LI Yao-hong School of Mathematics and Statistics Suzhou University Suzhou 234000 China

By using cone theory and the Monch fixed theorem combined with a monotone iterative technique,we investigate the existence of positive solutions for systems of secondorder nonlinear singular differential equations with integral boundary conditions on infinite interval and establish the existence theorem of positive solutions and iterative sequence for approximating the positive solutions.The results in this paper improve some known results.

关键词： boundary value problems positive solutions integral boundary conditions the Monch fixed point theorem

MODIFIED LEAST SQUARE METHOD ON COMPUTING DIRICHLET problems

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Annals of Differential Equations 2006年第3期22卷 350-355页

作者： Sheng Pingxing Tang Zhengquan (Dept. of Math., Shanghai University, Shanghai 200444)

The singularity theory of dynamical systems is linked to the numerical computation of boundary value problems of differential equations. It turns out to be a modified least square method for a calculation of variational problem defined on Ck(Ω), in which the base functions are polynomials and the computation of problems is transferred to compute the coefficients of the base functions. The theoretical treatment and some simple examples are provided for understanding the modification procedure of the methods. A modified least square method on difference scheme is introduced with a general matrix form of dynamical systems. We emphasize the simplicity of the algorithm and only use Euler algorithm to compute initial value problems of ODEs. A better algorithm is needed to reduce the stiffness of ODEs.

关键词： equilibria of dynamical systems sufficient and necessary condition on extremes calculus of variation boundary value problems modified least square method

EXISTENCE OF EXTREME SOLUTION TO FIRST-ORDER IMPULSIVE DIFFERENTIAL EQUATIONS WITH NONLINEAR boundary CONDITIONS

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Annals of Differential Equations 2011年第1期27卷 119-126页

作者： Huantao Zhu(Hunan College of Information,Changsha 410200)

This paper is concerned with the existence of extreme solutions to three-point boundary value problems with nonlinear boundary conditions for a class of first order impulsive differential equations. We obtain suficient conditions for the existence of extreme solutions by the upper and lower solutions method coupled with a monotone iterative technique.

关键词： impulsive differential equation monotone iterative technique boundary value problems

SOME RESULTS ON THE COEFFICIENTS OF INTEGRATED EXPANSIONS OF ULTRASPHERICAL POLYNOMIALS AND THEIR INTEGRALS

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Analysis in Theory and Applications 2001年第3期17卷 69-84页

作者： E.H.Doha S.I.EL-Soubhy Department of Mathematics Faculty of Science Cairo UniversityGiza-Egypt Department of Mathematics Girl's College of EducationJeddahSaudi Arabia

The formula of expressing the coefficients of an expansion ofultraspherical polynomials that has been integrated an arbitrary number of times in terms of the coefficients of the original expansion is stated in a more compact form and proved in a simpler way than the formula of Phillips and Karageorghis (1990). A new formula is proved for the q times integration of ultraspherical polynomials, of which the Chebyshev polynomials of the first and second kinds and Legendre polynomials are important special cases. An application of these formulae for solving ordinary differential equations with varying coefficients is discussed.CLC Number：O17 Document ID：AAuthor Resume：E. H. Doha，e-mail: eiddoha@frcu, eun. eg References：[1]Canuto,C. ,Spectral Methods in Fluid Dynamics,Springer,Belrin,1988.[2]Doha,E.H.,An Accurate Solution of Parabolic Equations by Expansion in Ultraspherical Polynomials,Comput. Math. Appl. ,19(1990),75-88.[3]Doha,E. H. ,The Coefficients of Differentiated Expansions and Derivatives of Ultraspherical Polynomials,Comput. Math. Appl.,21(1991),115-122.[4]Doha,E.H. ,The Chebyshev Coefficients of General order Derivatives of an Infinitely Differen-tiable Function in Two or Three Variables,Ann. Univ. Sci. Budapest. Sect. Comput. ,13(1992),83-91.[5]Doha,E. H.,On the Cefficients of Differentiable Expansions of Double and Triple Legendre Polynomials,Ann Univ. Sci. Budapest. Sect. Comput. ,15(1995),25-35.[6]Doha,E.H. ,The Ultraspherical Coefficients of the Moments of a General-Order Derivatives of an Infinitely Differentiable Function,J. Comput. Math. ,89(1998),53-72.[7]Doha,E.H. ,The Coefficients of Differentiated Expansions of Double and Triple Ultraspherical Polynomials,Annales Univ. Sci. Budapest.,Sect. Comp.,19(200),57-73.[8]Doha,E.H. and Al-Kholi,F. M. R. ,An Efficient Double Legerdre Spectral Method for Parabolic and Elliptic Partial Differential Equations,Intern. J. Computer. Math. (toAppear).[9]Fox,L. and Parker,I.B. ,Chebyshev Polynomials in Numerical Analysis,Clarendon Press,Oxford,1972.[10]Doha,E.H. an

关键词： differential equations Partial Differential Equations Spectral Methods Chebyshev polynomials Legendre polynomials Numerical Analysis boundary value problems Spectral Approximation Parabolic Equations Applied Mathematics Accurate Solution Fluid Dynamics Heat Transfer new formula Methods for