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

In this paper, the axisymmetric nonlinear stability of a clamped truncated shallow spherical shell with a nondeformable rigid body at the center under a concentrated load is investigated by use of the modified iteration method. The analytic formulas of second approximation for determining the upper and lower critical buckling loads are obtained.     

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

In this paper,the nonlinear stability problem of a clamped truncated shallow sphericalshell with a nondeformable rigid body at the center under a concentrated load is studied bymeans of the singular perturbation method.When the geometrical parameter k is large,theuniformly valid asymptotic solutions are obtained.     

ON THE NONLINEAR STABILITY OF A TRUNCATED SHALLOW SPHERICAL SHELL UNDER A UNIFORMLY DISTRIBUTED LOAD

A problem of practical interest for nonlioear axisymmetrical stability of a clamped truncated shallow spherical shell with a nondeformable rigid body under a uniformly distributed load is studied in this paper. By using modifled iteration method, some important analytic results are obtained and the corresponding numerical results are given in figures.     

THE FINITE ELEMENT METHOD OF SINGULAR PERTURBATION PROBLEM

In this paper we construct new finite element subspace using polynomials of different degrees and the new finite element scheme is established. The convergence of the scheme and the stability of the reduced difference equation are proved.     

ON SINGULAR PERTURBATION FOR A NONLINEAR INITIAL-BOUNDARY VALUE PROBLEM (Ⅱ)

In this paper, we consider a singularly perturbed problem of a kind of quasilinear hyperbolic-parabolic equations, subject to initial-boundary value conditions with moving boundary: When certain assumptions are satisfied and ε is sufficiently small, the solution of this problem has a generalized asymptotic expansion (in the Van der Corput sense), which takes the sufficiently smooth solution of the reduced problem as the first term, and is uniformly valid in domain Q where the sufficiently smooth solution exists. The layer exists in the neighborhood of t=0. This paper is the development of references [3–5]. The Project supported by the National Natural Science Foundation of China.     

ON SINGULAR PERTURBATION FOR A NONLINEAR INITIAL-BOUNDARY VALUE PROBLEM (Ⅱ)

In this paper, we consider a singularly perturbed problem of a kind of quasilinear hyperbolic-parabolic equations, subject to initial-boundary value conditions with moving boundary. When certain assumptions are satisfied and e is sufficiently small, the solution of this problem has a generalized asymptotic expansion (in the Van der Corput sense), which takes the sufficiently smooth solution of the reduced problem as the first term, and is uniformly valid in domain Q where the sufficiently smooth solutioh exists. The layer exists in the neighborhood of t=0. This paper is the development of references.     

APPLICATIONS OF THE EXTRAPOLATION METHOD TO THE NUMERICAL SOLUTION OF SINGULAR PERTURBATION PROBLEMS

In this paper we consider applications of extrapolation method to the numericalsolution of singular perturbation problem for elliptic—parabolic equation in order tomanifesting accuracy of approximations and estimate the order of accuracy,Concerningthe uniform convergence in ref.[1].its proof is given in the appendix.     

SINGULAR PERTURBATION FOR A NONLINEAR BOUNDARY VALUE PROBLEM OF FIRST ORDER SYSTEM

ＳＩＮＧＵＬＡＲＰＥＲＴＵＲＢＡＴＩＯＮＦＯＲＡＮＯＮＬＩＮＥＡＲＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＯＦＦＩＲＳＴＯＲＤＥＲＳＹＳＴＥＭＣｈｅｎＳｏｎｇｌｉｎ（陈松林）（ＲｅｃｅｉｖｅｄＡｐｒｉｌ８,１９８４;ＲｅｖｉｓｅｄＡｐｒｉｌ１５,１９...     

THE PERTURBATION SOLUTION OF THE LARGE ELASTIC CURVE OF BUCKLED BARS AND THE SINGULAR PERTURBATION METHOD FOR ITS IMPERFECT BIFURCATION PROBLEM

This paper presents the large deflection elastic curve of buckled bars throughperturbation method,and the bifurcation diagrams including the influence of theimperfection at the base by using singular perturbation method of imperfect bifurcationtheory.The physical meaning of the bifurcation diagrams is discussed.     

NON-SYMMETRICAL LARGE DEFORMATION OF A SHALLOW THIN SPHERICAL SHELL

ＮＯＮ－ＳＹＭＭＥＴＲＩＣＡＬＬＡＲＧＥＤＥＦＯＲＭＡＴＩＯＮＯＦＡＳＨＡＬＬＯＷＴＨＩＮＳＰＨＥＲＩＣＡＬＳＨＥＬＬＷａｎｇＸｉｎｚｈｉ（王新志）ＲｅｎＤｏｎｇｙｕｎ（任冬云）ＷａｎｇＬｉｎｘｉａｎｇ（王林祥）ＹｅｈＫａｉｙｕａｎ（叶开沅）（Ｇａｎ...     

A DIFFERENCE METHOD FOR SINGULAR PERTURBATION PROBLEM OF HYPERBOLIC-PARABOLIC PARTIAL DIFFERENTLAL EQUATION

In this paper we constructed an exponentially fitted difference scheme for singularperturbation problem of hyperbolic-parabolic partial differential equation.Not only do wetake a fitting factor in the equationm,but also we put one in the approximation of secondinitial condition.By means of the asymptotic solution of singular perturbation problem weproved the uniform convergence of this scheme with respect to the small parameter.     

SOME APPLICATIONS OF THE SINGULAR PERTURBATION METHOD TO THE BENDING PROBLEMS OF THIN PLATES AND SHELLS

This paper presents a review which tackles some nonlinear bending problems of plates and shells in a unified way by means of the technique of undetermined small parameters.     

PERTURBATION INITIAL PARAMETER METHOD FOR SOLVING THE GEOMETRICAL NONLINEAR PROBLEM OF AXISYMMETRICAL SHELLS

In the previous paper[7],the author presented a System of First-Order DifferentialEquations for theproblem of axisymmetrically loaded shells of revolution with small elastic.strains and arbitrarily large axial deflections.and a Method of Variable-CharacteristicNondimensionization with a Scale of Load Parameter.On this basis.by taking theweighted root-mean-square deviation of angular deflection from linearity as perturbationparameter.this paper pressents a perturbation system of nondimensional differentialequations for the problem,thus transforms the geometrical nonlinear problem into severallinear problems.This paper calculates these linear problems by means of the initialparameter method of numerical integration.The numerical results agree quite well with theexperiments.     

NONLINEAR AXISYMMETRIC BENDING AND STABILITY OF THIN SPHERICAL SHALLOW SHELL WITH VARIABLE THICKNESS UNDER UNIFORMLY DISTRIBUTED LOADS

In this paper, the nonlinear bending and stability of thin spherical shallow shell with variable thickness under uniformly distributed loads are investigated by a new modified iteration method proposed by Prof. Yeh Kai-yuan and the author. Deflections and critical loads have been calculated and the numerical results obtained have been given in figures and tabular forms. It is shown that the final equation determining the central deflection and the load obtained coincides with the cusp catastrophe manifold.     

THE APPLICATION OF MULTI－SCALE PERTURBATION METHOD TO THE STABILITY ANALYSIS OF PLANE COUETTE FLOW

ＴＨＥＡＰＰＬＩＣＡＴＩＯＮＯＦＭＵＬＴＩ－ＳＣＡＬＥＰＥＲＴＵＲＢＡＴＩＯＮＭＥＴＨＯＤＴＯＴＨＥＳＴＡＢＩＬＩＴＹＡＮＡＬＹＳＩＳＯＦＰＬＡＮＥＣＯＵＥＴＴＥＦＬＯＷＺｈｏｕＺｈｅ－ｗｅｉ（周哲玮）（ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｉｌｙ;Ｓｈａｇ...     

THE METHOD OF COMPOSITE EXPANSIONS APPLIED TO BOUNDARY LAYER PROBLEMS IN SYMMETRIC BENDING OF THE SPHERICAL SHELLS

In this paper,the method of composite expansions which was proposed by W.Z.Chien(1948)is extended to investigate two-parameter boundary layer problems.For the problems of symmetric deformations of the spherical shells under the action of uniformly distribution load q,its nonlinear equilibrium equations can be written as follows:where εand δare undetermined parameters.If δ=1 and εis a small parameter,the above-mentioned problem is called first boundary layer problem;if εis a small parameter,and δis a small parameter,too,the above-mentioned problem is called second boundary layer problem.For the above-mentioned problems,however,we assume that the constants ε,δand p satisfy the following equation:In defining this condition by using the extended method of composite expansions,we find the asymptotic solution of the above-mentioned problems with the clamped boundary conditions.     

THE BOUNDARY LAYER METHOD FOR THE SOLUTION OF SINGULAR PERTURBATION PROBLEM FOR THE PARABOLIC PARTIAL DIFFERENTIAL EQUATION

In this paper, we discuss the singular perturbation problem of the parabolic partialdifferential equation. As usual, we must reduce the mesh size in the neighbourhood of theboundary layer so that typical feature of the boundary layer will not be lost. Then we needvery large operational quantity when mesh sizes are getting too small.Now we propose the boundary layer scheme, which need not take very fine mesh size inthe neighbourhood of the boundary layer. Numerical examples show that the accuracy canbe satisfied with moderate step size.     

THE THEOREM OF THE STABILITY OF NONLINEAR NONAUTONOMOUS SYSTEMS UNDER THE FREQUENTLY-ACTING PERTURBATION—LIAPUNOV’S INDIRECT METHOD

In this paper the stability of nonlinear nonautonomous systems under the frequently-acting perturbation is studied.This study is a forward development of the study of thestability in the Liapunov sense;furthermore,it is of significance in practice sinceperturbations are often not single in the time domain.Malk in proved a general theoremabout thesubject.To apply the theorem,however,the user has to construct a Liapunovfunction which satisfies specified conditions and it is difficult to find such a function fornonlinear nonautonomous systems.In the light of the principle of Liapunov’s indirectmethod,which is an effective method to decide the stability of nonlinear systems in theLiapunov sense,the authors have achieved several important conclusions expressed in theform of theorems to determine the stability of nonlinear nonautonomous systems under thefrequently-acting perturbation.     

PERTURBATION METHOD TO SOLVE THE COUPLE PROBLEM AMONG HARMONIC WAVES

In this paper, in terms of the characteristics of weak coupling problems hetween different harmonic waves, a perturbation method was presented to solve the coupling problem among harmonic waves.     

PERTURBATION METHOD FOR REANALYSIS OF THE MATRIX SINGULAR VALUE DECOMPOSITION

The perturbation method for the reanalysis of the singular value decomposition(SVD)of general real matrices is presented in this paper.This is a simple but efficientreanalysis technique for the SVD,which is of great worth to enhance computationalefficiency of the iterative analysis problems that require matrix singular valuedecomposition repeatedly.The asymptotic estimate formulas for the singular values and thecorresponding left and right singular vectors up to second-order perturbation componentsare derived.At the end of the paper the way to extend the perturbation method to the case ofgeneral complex matrices is advanced.