Showing papers in "Applied Mathematics and Mechanics-english Edition in 1988"
TL;DR: In this paper, the buckling and postbuckling behavior of clamped circular cylindrical shells under lateral or hydrostatic pressure is studied applying singular perturbation method by taking deflection as perturbations parameter.
Abstract: Based on the boundary layer theory for the buckling of thin elastic shells suggested in ref. [14]. the buckling and postbuckling behavior of clamped circular cylindrical shells under lateral or hydrostatic pressure is studied applying singular perturbation method by taking deflection as perturbation parameter. The effects of initial geometric imperfection are also considered. Some numerical results for perfect and imperfect cylindrical shells are given. The analytical results obtained are compared with some experimental data in detail, which shows that both are rather coincident.
71 citations
TL;DR: In this article, the posibuckling behavior of simply supported rectangular plates under uniaxial compresion is investigated and the effects of initial imperfections are also studied.
Abstract: In this paper, applving perturbation method to von Karman nonlinear large deflection equations of plates by taking deflection as perturbation parameter, the posibuckling behavior of simply supported rectangular plates under uniaxial compresion is investigated. Two types of in-plane boundary conditions are now considered and the effects of initial imperfections are also studied. It is found that the theoretical results are in good agreement with experiments.
56 citations
TL;DR: Based on the generalized compatibility condition under constant and linear stress field, a quadrilateral generalized conforming isoparametric element, GC-Q6, was developed for plane stress analysis as mentioned in this paper.
Abstract: Based on the generalized compatibility condition under constant and linear stress field, a quadrilateral generalized conforming isoparametric element, GC-Q6, for plane stress analysis, is developed The element GC-Q6 can be regarded as an improved form of Wilson's non-conforming isoparametric element Q6 GC-Q6 can pass the patch test for arbitrary irregular mesh while Q6 can not GC-Q6 degenerates to Q6 when it is a parallelogram Numerical examples show that the GC-Q6 element gives more accurate stress solution than the existing non- conforming elements and is less sensitive to geometric distortion
30 citations
TL;DR: In this paper, the displacement solution method for the general bending problem of conical shells on the elastic foundation (Winkler Medium) is presented, where the governing differential equations in displacement form of the conical shell and by introducing a displacement function U(s, θ), the differential equations are changed into an eight-order soluble partial differential equation about the displacement function in which the coefficients are variable.
Abstract: The general bending problem of conical shells on the elastic foundation (Winkler Medium) is not solved. In this paper, the displacement solution method for this problem is presented. From the governing differential equations in displacement form of conical shell and by introducing a displacement function U(s, θ), the differential equations are changed into an eight-order soluble partial differential equation about the displacement function U(s, θ) in which the coefficients are variable. At the same time, the expressions of the displacement and internal force components of the shell are also given by the diplacement function U(s θ). As special cases of this paper, the displacement function introduced by V.S.Vlasov in circular cylindrical shell[5], the basic equation of the cylindrical shell on the elastic foundation and that of the circular plates on the elastic foundation are directly derived.
28 citations
TL;DR: In this paper, the analytic expression of the torsion function for a cylinder containing arbitrary oriented cracks is obtained, and the problem is reduced to solve a system of singular integral equations for the unknown dislocation density functions.
Abstract: In this paper, based on paper [1], the analytic expression of the torsion function for a cylinder containing arbitrary oriented cracks is obtained. The problem is reduced to solve a system of singular integral equations for the unknown dislocation density functions. Using the numerical method of the singular integral equations[2,7] the torsional rigidities and stress intensity factors are evaluated for several multicracked cylinders. Next, the creak-cutting method[5] is firstly extended to lve the torsion problem for a rectangular prism. The numerical results show that the method presented here is successful.
20 citations
TL;DR: In this paper, the authors solve axisymmetric problems by stress and deduce a series of valuable general solutions by unified method, and prove the completeness of these general solutions.
Abstract: In this paper we solve axisymmetric problems by stress and deduce a series of valuable general solutions by unified method. Some of them are well-known solutions, and others have not appeared in the literature. We also prove the completeness of these general solutions.
17 citations
TL;DR: In this paper, the expression of free energy is expanded in a power series, in which there aren't any terms of order higher than third in the temperature increments θ* and second in the strains γij in this paper.
Abstract: The expression of free energy is expanded in a power series, in which there aren't any terms of order higher than third in the temperature increments θ* and second in the strains γij in this paper. The regular patterns of the material coefficients changing with temperature increments can be derived from this expression, These regulations accord with the experimental graph in references but the constants in the expression of free energy must be determined by experimental data. It is pointed out that the variable modulus of elasticity E and shearing modulus of elasticity G are independent of each other, but the rest of the coefficients are related to them.
13 citations
TL;DR: In this paper, the characterizations of various probabilistically bounded sets are presented, and the linear operator theory and fixed point theory on probabilistic metric spaces are given, too.
Abstract: This paper is a continuation of the author's previous paper [1], in which the characterizations of various probabilistically bounded sets are presented, and the linear operator theory and fixed point theory on probabilistic metric spaces are given, too.
11 citations
TL;DR: In this paper, the minimum potential energy principle and stationary complementary energy principle for nonlinear elasticity with finite displacement, together with various complete and incomplete generalized principles were studied, however, the statements and proofs of these principles were not so clearly stated about their constraint conditions and their Euler equations.
Abstract: In a previous paper (1979)[1], the minimum potential energy principle and stationary complementary energy principle for nonlinear elasticity with finite displacement, together with various complete and incomplete generalized principles were studied. However, the statements and proofs of these principles were not so clearly stated about their constraint conditions and their Euler equations. In somecases, the Euler equations have been mistaken as constraint conditions. For example, the stress displacement relation should be considered as Euler equation in complementary energy principle but have been mistaken as constraint conditions in variation. That is to say, in the above mentioned paper, the number of constraint conditions exceeds the necessary requirement. Furthermore, in all these variational principles, the stress-strain relation never participate in the variation process as constraints, i.e., they may act as a constraint in the sense that, after the set of Euler equations is solved, the stress-strain relation may be used to derive the stresses from known strains, or to derive the strains from known stresses. This point was not clearly mentioned in the previous paper (1979)[1]. In this paper, the high order Lagrange multiplier method (1983)[2] is used to construct the corresponding generalized variational principle in more general form. Throughout this paper, V/.V. Novozhilov's results (1958)[3] for nonlinear elasticity are used.
10 citations
TL;DR: In this article, sufficient conditions of the instability for the third order linear differential equation with varied coefficient, at least one of the characteristic roots of which has positive real part, by means of Liapunov's second method were given.
Abstract: In reference [1] asymptotic stability of dynamic system with slowly changing coefficients for all characteristic roots which have negative real part has been proved by means of Liapunov's second method. In this paper, we give some sufficient conditions of the instability for the third order linear differential equation with varied coefficient, at least one of the characteristic roots of which has positive real part, by means of Liapunov's second method.
8 citations
TL;DR: The generalized Sobolev embedding theorem and the generalized Rellich-Kondrachov compact theorem for finite element spaces with multiple sets of functions are established in this article.
Abstract: In this paper, the generalized Sobolev embedding theorem and the generalized Rellich-Kondrachov compact theorem for finite element spaces with multiple sets of functions are established. Specially, they are true for nonconforming, hybrid and quasi-conforming element spaces with certain conditions.
TL;DR: In this paper, the deformations and stability of large axisymmetric deflection of spherical caps under centrally distributed pressures are investigated. And the influence of the buckling modes on the critical loads is analyzed.
Abstract: In this paper the deformations and stability in large axisymmetric deflection of spherical caps under centrally distributed pressures are investigated. The Newton- spline method for solving the nonlinear equations governing large axisymmetric deflection of spherical caps is presented. The buckling behavior is studied for a cap with fixed geometry when the size of the loaded radius is allowed to vary, and for a fixed loaded radius when the shell geometry is allowed to vary. The influence of the buckling modes on the critical loads is analysed. Numerical results are given for ν=0.3.
TL;DR: In this article, the Fourier series of rational fractions of Jacobian elliptic functions is used for the detection and study of chaotic behavior and subharmonic bifurcations in a two-dimensional Hamiltonian system subject to external periodic forcing by Melnikov's method.
Abstract: In this paper more than ninety of the Fourier series of rational fractions of Jacobian elliptic functions sn(u.k.), cn(u.k) and dn(u.k) are listed, which cannot be found in the handbook[1] and Ref. [2]. For the detection and study of chaotic behavior and subharmonic bifurcations in a two-dimensional Hamiltonian system subject to external periodic forcing by Melnikov's method, and for study of some problems of physical science and engineering. these formulas can be used.
TL;DR: In this paper, the existence and asymptotic behavior of vector boundary value problems are proved by constructing special invariant regions in which solutions display so-called boundary layer phenomena and angular layer phenomena.
Abstract: In this paper we consider singular perturbed phenomena of semilinear second order systems, under appropriate assumptions, the existence and asymptotic behavior as e→0+of solution of vector boundary value problem are proved by constructing special invariant regions in which solutions display so-called boundary layer phenomena and angular layer phenomena.
Journal Article•
TL;DR: In this article, a barotropic semi-geostrophic model with topographic forcing the stability and solutions of the nonlinear Rossby waves are discussed using the KdV equation.
Abstract: Using a barotropic semi-geostrophic model with topographic forcing the stability and solutions of the nonlinear Rossby waves are discussed. It is found that the effects of the W-E oriented topography and the N-S oriented topography on the stability and phase speed of the waves are quite different. It is also found that the nonlinear Rossby waves forced by the topography can be described by the well-known KdV equation.
TL;DR: In this article, the combined KdV equation can be reduced to the Painleve equation, and a new partial differential equation was derived by utilizing the transformation of similarity variables.
Abstract: In this paper, we discuss a property of solitary wave solutions of the combined KdV equation. Meantime, we point out that the combined KdV equation can be reduced to the Painleve equation. Furthermore, utilizing special transformations of similarity variables, we derive a kind of new partial differential equations.
TL;DR: In this paper, the axially symmetric torsion of rigid circular shaft of varying diameter embedded in an elastic half space is studied by line-loaded integral equation method (LLIEM), where the problem is formulated by distributions of ficitious fundamental loads along the axis of symmetry in interval of the shaft and is reduced to a one-dimensional and non-singular Fredholm integral equation of the first kind and is easily solved numerically.
Abstract: The axially symmetric torsion of rigid circular shaft of varying diameter embedded in an elastic half space is studied by line-loaded integral equation method (LLIEM), where the problem is formulated by distributions of ficitious fundamental loads PRCHS (point ring couple in half space) along the axis of symmetry in interval of the shaft and is reduced to a one-dimensional and non-singular Fredholm integral equation of the first kind and is easily solved numerically. Numerical examples of torsin of rigid conic, cylinder, conical-cylinder embedded in an elastic half space are given and compared with the known result obtained by the others. The exact solution of torsion of rigid half sphere embedded in an elastic half space is also presented.
TL;DR: In this article, the discontinuity of stresses and strains at interlaminar surfaces of the composue laminate and a variational principle corresponding to the 3D laminate theory is developed.
Abstract: This paper discusses the discontinuity of stresses and strains at interlaminar surfaces of the composue laminate and presents a 3-D laminate theory for composite materials. This paper also presents a new type of elastic energy based on the globally continuous variables in laminates, different from the traditional potential energy and complementary energy. Then, a variational principle corresponding to the 3-D laminate theory is developed. The theory and the principle could be a basis of verifying the 2-D laminate theory and determining the interlaminar stresses near the free edges.
TL;DR: In this paper, the existence and uniqueness of the limit cycle for a general predator-prey system was proved and another theorem on the existence of closed trajectories for the same model was proved.
Abstract: In this paper we prove a theorem, theorem 2, on nonexistence of closed trajectory for a general predator-prey system. Then, using this theorem and another theorem on existence and uniqueness of limit cycle for predator-prey system, we complete the investigation of a concrete model of predator-prey system
$$\begin{gathered} \dot x = \gamma x({{1 - x} \mathord{\left/ {\vphantom {{1 - x} K}} \right. \kern-
ulldelimiterspace} K}) - {{yx^n } \mathord{\left/ {\vphantom {{yx^n } {(a + x^n )}}} \right. \kern-
ulldelimiterspace} {(a + x^n )}} \hfill \\ \dot y = y({{\mu x^n } \mathord{\left/ {\vphantom {{\mu x^n } {(a + x^n ) - D}}} \right. \kern-
ulldelimiterspace} {(a + x^n ) - D}}) (n = 1,2) \hfill \\ \end{gathered} $$
under the conditions of all kinds of parameters.
TL;DR: In this paper, a class of three level explicit schemes for a dispersive equation with stability condition |r|=|α|Δt/(Δx)3≤2.382484, are considered.
Abstract: In this paper, a class of three level explicit schemes for a dispersive equation ut=auxxx with stability condition |r|=|α|Δt/(Δx)3≤2.382484, are considered. The stability condition for this class of schemes is much better than |r|≤0.3849 in [1], [2] and |r|≤0.701659 in [3], and |r|≤1.1851 in [4].
TL;DR: In this article, a nonlinear axisymmetrical stability of a clamped truncated shallow spherical shell with a nondeformable rigid body under a uniformly distributed load is studied.
Abstract: A problem of practical interest for nonlinear 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 modified iteration method, some important analytic results are obtained and the corresponding numerical results are given in figures.
TL;DR: In this paper, it has been shown that the undetermined multipliers in the equations of impact can be cancelled for both the generalized coordinates and the quasi-coordinates, thus there are only n-p equation of impact.
Abstract: In order to solve the problem of motion for the system with n degrees of freedom under the action of p impulsive constraints, we must solve the simultaneous equations consisting of n+p equations. In this paper, it has been shown that the undetermined multipliers in the equations of impact can be cancelled for the cases of both the generalized coordinates and the quasi-coordinates. Thus there are only n-p equations of impact. Combining these equations with p impulsive constraint equations, we have simultaneous equations consisting of n equations. Therefore, only n equations are necessary to solve the problem of impact for the system subjected to impulsive constraints. The method proposed in this paper is simpler than ordinary methods.
TL;DR: In this paper, the conceptual root of the current incorrect mechanical interpretation of the spin in continuum was investigated, and the correct one was found out by the authors of the present paper.
Abstract: The present paper investigates the conceptual root of the current incorrect mechanical interpretation of the spin in continuum and gives the correct one.
TL;DR: In this paper, a general solution of differential equation for lateral displacement lunction of rectangular elastic thin plates in free vibration is established, which can be used to solve the vibration problem of rectangular plate with arbitrary boundaries.
Abstract: A general solution of differential equation for lateral displacement lunction of rectangular elastic thin plates in free vibration is established in this paper. It can be used to solve the vibration problem of rectangular plate with arbitrary boundaries. As an example, the frequency and its vibration mode of a rectangular plate with four edges free have been solved.
TL;DR: In this article, the minimum critical load of cantilever rectangular plates under a concentrated force, a uniformly distributed load, a distributed load in triangular form and a concentrated couple, respectively, is discussed.
Abstract: The present article researches several problems about the lateral instability, of cantilever plates by means of the energy method, in which we discuss the minimum critical load of cantilever rectangular plates under a concentrated force, a uniformly distributed load, a distributed load in triangular form and a concentrated couple, respectively, when the lateral buckling takes place.
TL;DR: In this article, 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.
Abstract: 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.
TL;DR: In this paper, the transient spherical flow behavior of a slightly compressible non-Newtonian, power-law fluids in porous media is studied and a nonlinear partial differential equation of parabolic type is derived.
Abstract: The transient spherical flow behavior of a slightly compressible non-Newtonian, power-law fluids in porous media is studied. A nonlinear partial differential equation of parabolic type is derived. The diffusivity equation for spherical flow is a special case of the new equation. We obtain analytical, asymptotic and approximate solutions by using the methods of Laplace transform and weighted mass conservation. The structures of asymptotic and approximate solutions are similar, which enriches the theory of one-dimensional flow of non-Newtonian fluids through porous media.
TL;DR: In this paper, the problem of the bending, stability and vibrations of the rectangular plates with free boundaries on elastic foundations was discussed, and a flexural function was selected which satisfies not only all the boundary conditions of free edges but also the conditions at free corner points, and consequently a better approximate solution was obtained.
Abstract: This paper discusses the problems of the bending, stability and vibrations of the rectangular plates with free boundaries on elastic foundations. In the present paper we select a flexural function, which satisfies not only all the boundary conditions of free edges but also the conditions at free corner points, and consequently we obtain a better approximate solution. The energy method is used in this paper.
TL;DR: In this paper, a general analytical method based on Ref. [1] is presented to study the bending vibration of an elliptical column partially submerged in water, and it is pointed out that there is a limitation to the method mentioned in Ref.
Abstract: In this paper, a general analytical method based on Ref. [1] is presented to study the bending vibration of an elliptical column partially submerged in water. Besides, it is pointed out that there is a limitation to the method mentioned in Ref. [2]. As a special example, the natural frequencies of circular column submerged in water considering compressibility are calculated, and the extent of compressible effect is given.