Showing papers in "Applied Mathematics and Mechanics-english Edition in 1990"
TL;DR: The main purpose of this paper is devoted to generalizing the results of Browder[1,2] as discussed by the authors, which consists of four parts: in the first part, we introduce the concepts of multivalued (S) and (S)-type mappings, and in the second part we define the pseudo-degree for (S-) type mappings and the degree for(S)+type mapping, all the generalizations of the degree defined by Browder
Abstract: The main purpose of this paper is devoted to generalizing the results of Browder
[1,2].
This paper consists of four parts. In the first part, we introduce the concepts of multivalued (S) and (S) type mappings and the concepts of the limits of multivalued (S) and (S) type mappings. These kinds of mappings contain many monotone type mappings, such as maximal monotone mapping, bounded pseudo-monotone mapping and bounded generalized pseudo-monotone mapping, as its special cases. In the second part we define the pseudo-degree for (S) type mapping and the degree for (S)
+
type mapping. These two kinds of degrees are all the generalizations of the degree defined by Browder
[1,2].As applications, we utilize the degree theory presented in part 2 to study the existence of solutions for the multivalued operator equations (see part 3) and to obtain some new fixed point theorems in part 4.
25 citations
TL;DR: In this article, the exact solutions for stationary responses of one class of the second order and three classes of higher order nonlinear systems to parametric and/or external white noise excitations are constructed by using Fokker-Planck-Kolmogorov equation approach.
Abstract: The exact solutions for stationary responses of one class of the second order and three classes of higher order nonlinear systems to parametric and/or external white noise excitations are constructed by using Fokker-Planck-Kolmogorov equation approach. The conditions for the existence and uniqueness and the behavior of the solutions are discussed. All the systems under consideration are characterized by the dependence of nonconservative forces on the first integrals of the corresponding conservative systems and are called generalized-energy-dependent (G.E.D.) systems. It is shown taht for each of the four classes of G.E.D. nonlinear stochastic systems there is a family of non-G.E.D. systems which are equivalent to the G.E.D. system in the sense of having identical stationary solution. The way to find the equivalent stochastic systems for a given G.E.D. system is indicated and as an example, the equivalent stochastic systems for the second order G.E.D. nonlinear stochastic system are given. It is pointed out and illustrated with example that the exact stationary solutions for many non-G.E.D. nonlinear stochastic systems may be found by searching the equivalent G.E.D. systems.
24 citations
TL;DR: In this paper, the authors established the topological rules adapting to analysing the skin-friction lines and the section streamlines in cascades, and showed that the number of nodal points equals the saddle points on the skinfriction line vector fields in each pitch range.
Abstract: Based on the working of Lighthill and Hunt et al., in the present paper the author has established the topological rules adapting to analysing the skin-friction lines and the section streamlines in cascades. These rules are (1) for a rotor cascade without shroud band, the total number of nodal points equals that the saddle points on the skin-friction line vector fields in each pitch range; (2) for an annular or straight cascade with no clearances at blade ends, the total number of saddle points is two more than that of nodal points on the skin-friction line fields in a pitch; (3) the total number of saddles in the secondary flow fields on cross-sections in cascade is one less than that of nodes; (4) in the section streamline vector fields on a meridian surface penetrating a flow passage, and on leading and trailing edge sections, the total number of nodes is equal to that of saddles; (5) on the streamline vector fields of a blade-to-blade surface, the total number of nodes is one less than that of saddles.
22 citations
TL;DR: In this article, the buckling and postbuckling behaviors of perfect and imperfect antisymmetrically angle-ply laminated composite plates under uniaxial compression were studied by perturbation technique which takes deflection as its perturbance parameter.
Abstract: The buckling and postbuckling behaviors of perfect and imperfect antisymmetrically angle-ply laminated composite plates under uniaxial compression have been studied by perturbation technique which takes deflection as its perturbation parameter.
21 citations
TL;DR: In this paper, the basic differential equations for finite deflections of elastic plates according to Reissner's approximate stress distributions are given and the buckling and postbuckling problems of elastic rectangular plates, including the effect of transverse shear deformation, are solved and discussed.
Abstract: This paper gives the basic differential equations for finite deflections of elastic plates according to Reissner's approximate stress distributions. The buckling and postbuckling problems of elastic rectangular plates, including the effect of transverse shear deformation, are solved and discussed, by using perturbation method suggested in ref. [8]. The postbuckling equilibrium paths of perfect and imperfect moderately thick rectangular plates are presented and compared with the results based on thin plate theory.
16 citations
TL;DR: In this article, the modified iteration method is successfully extended to investigate the nonlinear free vibration of corrugated circular plates with full corrugations, and the analytical relation for the amplitude-frequency response is obtained.
Abstract: In this paper, the modified iteration method is successfully extended to investigate the nonlinear free vibration of corrugated circular plates with full corrugations. The analytical relation for the amplitude-frequency response of corrugated circular plates is obtained and discussions on the influences of geometrical parameters on vibration behaviours of corrugated circular plates are made. The present results are practically important in the design of elastic elements in precision instruments.
13 citations
TL;DR: In this article, the convexity of the variational functionals are closely related to a so-called gap function, which plays an important role in nonlinear variational problems.
Abstract: Dual variational extremum principles for rate problems of classical elastoplasticity at finite deformation are studied in Updated Lagrangian rate forms. It is proved that the convexity of the variational functionals are closely related to a so-called gap function, which plays an important role in nonlinear variational problems.
11 citations
TL;DR: In this paper, the Gibbs-Appell's equations of motion were extended to the most general variable mass nonholonomic mechanical systems and an integral variational principle was obtained for non-holonomic systems.
Abstract: In this paper, the Gibbs-Appell's equations of motion are extended to the most general variable mass nonholonomic mechanical systems. Then the Gibbs-Appell's equations of motion in terms of generalized coordinates or quasi-coordinates and an integral variational principle of variable mass nonlinear nonholonomic mechanical systems are obtained. Finally, an example is given.
10 citations
TL;DR: In this article, the authors introduce the concept of generalized KKM mapping and obtain some general version of the famous K-KM theorem and Ky Fan's minimax inequality.
Abstract: The purpose of this paper is to introduce the concept of generalized KKM mapping and to obtain some general version of the famous KKM theorem and Ky Fan's minimax inequality. As applications, we utilize the results presented in this paper to study the saddle point problem and the existence problem of solutions for a class of quasi-variational inequalities. The results obtained in this paper extend and improve some recent results of [1–6].
9 citations
TL;DR: In this article, the general equations of equilibrium for axisymmetrical deformation including the torsional deformation of revolutional shells are derived and it is shown that the shearing stress distribution due to torsion is independent of other stress components including those of membrane stress and bending stress.
Abstract: In this paper, the general equations of equilibrium for axisymmetrical deformation including the torsional deformation of revolutional shells are derived. It is shown that the shearing stress distribution due to torsion is independent of other stress components including those of membrane stress and bending stress.
In this paper, the torsional deformation is considered to be represented by membrane action only, and also by the combined action of bending membrane deformation. It is shown that the main contribution of torsional rigidity is that related to membrane action.
7 citations
TL;DR: In this paper, a perturbation technique for the buckling and postbuckling of rectangular plates under inplane compression has been proposed, which takes deflection as its perturbance parameter.
Abstract: Full-range analysis for the buckling and postbuckling of rectangular plates under inplane compression has been made by perturbation technique which takes deflection as its perturbation parameter.
TL;DR: In this article, a kind of rationalism theory of shell is established which is of different mechanic characters in tension and in compression, and the finite element numerical analysis method is also described.
Abstract: In this paper a kind of rationalism theory of shell is established which is of different mechanic characters in tension and in compression, and the finite element numerical analysis method is also described.
TL;DR: In this article, the skin-friction line patterns on compressor and turbine cascade surfaces are depicted and the streamline patterns of the secondary flow fields in the cross-section of a curved pipe and a turbine cascade are drawn under given conditions.
Abstract: With an application of topological analysis, in this paper the skin-friction line patterns on compressor and turbine cascade surfaces are depicted and the streamline patterns of the secondary flow fields in the cross-section of a curved pipe and a turbine cascade are drawn under given conditions. In addition the structures of vortices within three-dimensional viscous flow fields in cascades are analysed.
TL;DR: Based on the von Karman-type theory of plates, nonlinear bending problems of simply supported symmetric laminated cross-ply rectangular plates under the combined action of pressure and inplane load are investigated in this paper.
Abstract: Based on the von Karman-type theory of plates, nonlinear bending problems of simply supported symmetric laminated cross-ply rectangular plates under the combined action of pressure and inplane load are investigated in this paper. The solution which satisfies the governing equations and boundary conditions is obtained by using the double Fourier series method.
TL;DR: In this article, a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed and an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given.
Abstract: In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.
TL;DR: In this paper, a group of stress functions has been proposed for the calculation of a crack emanating from a hole with different shape (including circular, elliptical, rectangular, or rhombic hole) by boundary collocation method.
Abstract: In this paper a group of stress functions has been proposed for the calculation of a crack emanating from a hole with different shape (including circular, elliptical, rectangular, or rhombic hole) by boundary collocation method. The calculation results show that they coincide very well with the existing solutions by other methods for a circular or elliptical hole with a crack in an infinite plate. At the smae time, a series of results for different holes in a finite plate has also been obtained in this paper. The proposed functions and calculation procedure can be used for a plate of a crack emanating from an arbitrary hole.
TL;DR: In this paper, the authors analyzed the noise at inception and collapse of an isolated bubble cavity filled with gas and vapour, and their numerical solutions of the sound pressure and the vibration velocity were presented.
Abstract: The paper analyzes the noise at inception and collapse of an isolated bubble cavity filled with gas and vapour. The expressions and their numerical solutions of the sound pressure and the vibration velocity are presented.
TL;DR: In this article, the free bending vibration of a cylindrical tank partially filled with liquid and submerged in water was studied. And the analysis showed that the effect of liquid and water on the vibration of the tank is equivalent to a generalized distributive mass attached to the tank.
Abstract: This paper studies the free bending vibration of cylindrical tank partially filled with liquid and submerged in water. The depths of liquid and water may be completely arbitrary. The exact calculating formulae of mode shape functions and inherent frequencies are deduced. The results can be gained by means of computer. The analysis shows that the effect of liquid and water on vibration of cylindrical tank is respectively equivalent to a generalized distributive mass attached to the tank.
TL;DR: In this paper, a line-loaded integral equation (LLIEM) method was proposed to solve the torsion problem of an elastic shaft of revolution embedded in an elastic half space.
Abstract: The problem of torsion of elastic shaft of revolution embedded in an elastic half space is studied by the Line-Loaded Integral Equation Method (LLIEM). The problem is reduced to a pair of one-dimensional Fredholm integral equations of the first kind due to the distributions of the fictitious loads “Point Ring Couple (PRC)” and “Point Ring Couple in Half Space (PRCHS)” on the axis of symmetry in the interior and external ranges of the shaft occupied respectively. The direct discrete solution of this integral equations may be unstable, i.e. an ill-posed case occurs. In this paper, such an ill-posed Fredholm integral equation of first kind is replaced by a Fredholm integral equation of the second kind with small parameter, which provides a stable solution. This method is simpler and easier to carry out on a computer than the Tikhonov's regularization method for ill-posed problems. Numerical examples for conical, cylindrical, conical-cylindrical, and parabolic shafts are given.
TL;DR: In this paper, a multi-cost-functional method for solving inverse problems of wave equations is introduced, which has the advantage of being programmed for two- or three-dimensional problems as well as for one-dimensional ones.
Abstract: We introduce a multi-cost-functional method for solving inverse problems of wave equations. This method has its simplicity, efficiency and good physical interpretation. It has the advantage of being programmed for two- or three- (space) dimensional problems as well as for one-dimensional problems.
TL;DR: In this article, the authors extended the results of [1] and pointed out that there may exist as many as fourteen bifurcation diagrams which are not topologically equivalent to each other.
Abstract: The authors of [1] discussed the subharmonic resonance bifurcation theory of nonlinear Mathieu equation and obtained six bifurcation diagrams in (α,β) -plane. In this paper, we extended the results of [1] and pointed out that there may exist as many as fourteen bifurcation diagrams which are not topologically equivalent to each other.
TL;DR: On the assumption that the yield criterion of orthotropic materials is isomorphic with Huber-Mises criterion of isotropic materials, this article put forward a dimensionless stress yield criterion, and obtained the associated plastic flow law.
Abstract: On the assumption that the yield criterion of orthotropic materials is isomorphic with Huber-Mises criterion of isotropic materials, we put forward a dimensionless stress yield criterion, and obtained the associated plastic flow law. Using experimental stress-strain curves in various simple stress states, generalized effective stress-strain formulae may be derived correspondingly in various forms.
TL;DR: In this paper, the authors generalize the concept of anisotropy degree of linearly elastic solids to nonlinear and non-elastic solids, and define anisotropic degrees for both types of solids.
Abstract: This research aims at the generalization of the concept of anisotropy degree of linearly elastic solids which has been defined and investigated in detail by Zhang [1988] to that of nonlinear and non-elastic solids. The properties of the anisotropy degrees defined here show that they are reasonable.
TL;DR: In this article, an accurate solution for the thick rectangular plate with free edges laid on elastic foundation is presented using the superposition method of trigonometric series, which can solve this kind of plates directly and simply.
Abstract: In this paper an accurate solution for the thick rectangular plate with free edges laid on elastic foundation is presented. The superposition method of trigonometric series is used. The method can solve this kind of plates directly and simply. Its results completely satisfy the boundary conditions of the four free edges and nicely agree with the solutions by Wang Ke-lin and Huang Yi[2].
TL;DR: In this paper, an estimate to the maximum modulus is made for a special case of quasi-linear elliptic equations, i.e., the solutions of B satisfy the following structural conditions:
Abstract: Let G be a bounded domain in E
n
.Consider the following quasi-linear elliptic equation
Although the boundedness of generalized solutions of the equation is proved for very general structural conditions, it does not supply a priori estimate for maximum modulus of solutions. In this paper an estimate to the maximum modulus is made firstly for a special case of quasi-linear elliptic equations, i.e. the
$$\overrightarrow A $$
and B satisfy the following structural conditions:
TL;DR: In this article, a uniform second-order difference scheme for a class of boundary value problems of fourth-order ODEs is presented. And a numerical example of such a scheme is given.
Abstract: In this paper, we construct a uniform second-order difference scheme for a class of boundary value problems of fourth-order ordinary differential equations. Finally, a numerical example is given.
TL;DR: In this article, a catastrophic model of vibrational buckling of elastic arches is presented, and the critical condition of losing stability is given, based on the catastrophes.
Abstract: This paper represents an attempt at the application of catastrophe theory to the dynamic stability of engineering structures. The authors not only obtain a catastrophic model of vibrational buckling of elastic arches, but also give the critical condition of losing stability.
TL;DR: In this article, a variational calculus and smeared-stiffener theory were used for finite deflection of closely stiffened truncated laminated composite conical shells under arbitrary loads.
Abstract: A Donnell type theory is developed for finite deflection of closely stiffened truncated laminated composite conical shells under arbitrary loads by using the variational calculus and smeared-stiffener theory. The most general bending-stretching coupling and the effect of eccentricity of stiffeners are considered. The equilibrium equations, boundary conditions and the equation of compatibility are derived. The new equations of the mixed-type of stiffened laminated composite conical shells are obtained in terms of the transverse deflection and stress function. The simplified equations are also given for some commonly encountered cases.
TL;DR: In this article, the kinematically admissible velocity field with surface crack on forward extruding bar is put forward during the axisymmetric cup-bar combined extrusion process, in accordance with the results of model experiments.
Abstract: In this paper, the kinematically admissible velocity field with surface crack on forward extruding bar is put forward during the axisymmetric cup-bar combined extrusion process, in accordance with the results of model experiments.
TL;DR: In this paper, boundary element-linear complementary equations are formulated to solve elastic contact problems with Coulomb frictions, and a new attempt is made to solve free boundary problems in solid mechanics by means of boundary elementmathematical programming techniques.
Abstract: Boundary element-linear complementary equations are formulated to solve elastic contact problems with Coulomb frictions. It is also a new attempt to solve free boundary problems in solid mechanics by means of boundary element-mathematical programming techniques.