Showing papers in "Applied Mathematics and Mechanics-english Edition in 1995"
TL;DR: In this article, the governing equations of the free vibrations of spherical and cylindrical shells with a regular singularity, are solved by Frobenius Series Method in the form of matrix.
Abstract: The governing equations of the free vibrations of spherical and cylindrical shells with a regular singularity, are solved by Frobenius Series Method in the form of matrix. Considering the relationship of the roots of the indicial equation, we get some various expressions of solutions according to different cases. This work lays a foundation of solving certain elastic problems by analytical method.
26 citations
TL;DR: In this article, the authors used the complex function method for solving the problem of interaction of plane SH-waves and circular cavity surfaced with lining in anisotropic media, which can be used to simulate the conditions of the geology.
Abstract: In this paper, we use the complex function method for solving the problem of interaction of plane SH-waves and circular cavity surfaced with lining in anisotropic media. Anisotropic media can be used to simulate the conditions of the geology. This problem can be handled by using the method similar to that incorporated in Ref. [5] to define the scattering waves in media, added with the given boundary condition of the circular cavity.
18 citations
TL;DR: In this paper, the authors employed the fractional calculus approach to study second fluid flow in a pape and derived the analytical solution which the derivate order is half and verified the reliability of Laplace numerical inversion based on Crump algorithm for the problem.
Abstract: It is more satisfactory for fluid materials between viscous and elastic to introduce the fractional calculus approach into the constitutive relationship. This paper employs the fractional calculus approach to study second fluid flow in a pape. First, we derive the analytical solution which the derivate order is half and then with the analytical solution we verify the reliability of Laplace numerical inversion based on Crump algorithm for the problem, and finally we analyze the characteristics of second order fluid flow in a pipe by using Crump method. The results indicate that the more obvious the viscoelastic properties of fluid is, the more sensitive the depondence of velocity and stress on fractional derivative order is.
18 citations
TL;DR: In this paper, the authors introduced the concept of the Z-M-PN space and obtained some new fixed point theorems in probabilistic metric spaces, such as the fixed point theorem of Schauder, Guo's theorem and Petryshyn's theorem.
Abstract: In this paper, we introduce the concept of the Z-M-PN space, and obtain some new fixed point theorems in probabilistic metric spaces. Meanwhile, some famous fixed point theorems are generalized in probabilistic metric spaces, such as fixed point theorem of Schauder, Guo's theorem and fixed point theorem of Petryshyn are generalized in Menger PN-space. And fixed point theorem of Altman is also generalized in the Z-M-PN space.
16 citations
TL;DR: In this article, a method to study the stability of nonholonomic systems with respect to partial variables is given and several stability theorems of non-holonomic non-homonomic systems are obtained.
Abstract: In this paper, a method to study the stability of nonholonomic systems with respect to partial variables is given and several stability theorems of nonholonomic systems with respect to partial variables are obtained. Moreover, a relationship between the stability of a nonholonomic system with respect to all variables and that to partial variables is obtained.
15 citations
TL;DR: Based on the nonlinear characters of the discrete problems of some elliptical variational inequalities, this paper presented a numerical iterative method, the schemes of which are pithy and converge rapidly.
Abstract: Based on the nonlinear characters of the discrete problems of some elliptical variational inequalities, this paper presents a numerical iterative method, the schemes of which are pithy and converge rapidly. The new method possesses a high efficiency in solving such applied engineering problems as obstacle problems and free boundary problems arising in fluid lubrications.
15 citations
TL;DR: In this paper, the existence of exponential attractors for a generalized Ginzburg-Landau equation in one dimension was proved based on the exponential attractor theory. But it was not shown that these attractors can be used to obtain a generalized GLE equation in the one dimension.
Abstract: Based on the paper [1], we obtain the existence of exponential attractors for a generalized Ginzburg-Landau equation in one dimension
14 citations
TL;DR: In this paper, a new systematic analysis method-remaider effect analysis (abbr. REAM) is proposed by means of the modified partial differential equations of finite difference schemes.
Abstract: In the present paper, two contents are enclosed. First. the Fourier analysis approac.h of the dispersion relation and group velocio, effect of .finite difference schemes is discussed, the defects of the approach is pointed out and the correction is made; Second, a new systematic analysis method-remaider-effect analysis (abbr. REAM) is proposed by means of the modified partial differential equations (abbr. MPDE) of finite difference schemes. The analysis is based on the synthetical stud), of the rational dispersion-and dissipation relations of finite difference schemes. And the method clearly possesses constructivity.
13 citations
TL;DR: In this article, a thermal postbuckling analysis for a moderately thick rectangular plate subjected to uniform and non-uniform tent-like temperature loading and combined axial compression and uniform temperature loading is presented.
Abstract: A thermal postbuckling analysis is presented for a moderately thick rectangular plate subjected to (1) uniform and non-uniform tent-like temperature loading; and (2) combined axial compression and uniform temperature loading. The initial geometrical imperfection of plate is taken into account. The formulations are based on the Reissner-Mindlin plate theory considering the effects of rotary inertia and transverse shear deformation. The analysis uses a deflection-type perturbation technique to determine the thermal buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of perfect and imperfect, moderately thick rectangular plates and are compared with the results predicted by the thin plate theory.
10 citations
TL;DR: In this paper, an analytical method is used for the problem of scattering of plane SH-waves by multiple shallow circular-arc cangons, and the solution of the problem is finally reduced to solving a set of infinite algbraic equations.
Abstract: The analytical method is used for the problem of scattering of plane SH-waves by multiple shallow circular-arc cangons. The solution of multiple scattering of plane SH-waves is first expressed as the sum of series of solutions in each of local coordinates using separation of variables and is then converted into the form of dual infinite series of a local coordinate sytem by Graf's addition formula suitable for the interior and exterior problems. The solution of the problem is finally reduced to solving a set of infinite algbraic equations. Numerical results of scattering influence on the motion on the earth surface are presented for the two adjacent shallow circular-are canyons with the same diameter and variable depth-to-width ratio, and the effect of screening and interaction between canyons are discussed in the paper.
9 citations
TL;DR: The results show that the motion includes certain characteristics of reverse transformation the counter clockwise rotation can be developed into clockwise, and vice versa; the convergence can be changed into divergence through blow-up, and the divergence will die out continuously.
Abstract: From the pansystems view of prediction, the paper investigates the blow-up and post blow-up of fluid in rotation and convergence. The results show that the motion includes certain characteristics of reverse transformation the counter clockwise rotation can be developed into clockwise, and vice versa; the convergence can be changed into divergence through blow-up, and the divergence will die out continuously. The real forecasting must look this mechanism in the face. Generally speaking, the forecasting of evolution for fluid can't be considered only as traditional Cauchy problem. The traditional forecasi models should be rediscussed questioningly.
TL;DR: In this article, the problem of bending a rectangular plate with three clamped edges and one free edge under uniformly distributed load is solved by the reciprocal theorem method (RTM) based on Reissner's theory.
Abstract: In this paper, reciprocal theorem method (RTM) is generalized to solve the problems of bending of thick rectangular plates based on Reissner’s theory. First, the paper gives the basic solution of the bending of thick rectangular plates: and then the exact analytical solution of the bending of thick rectangular plate with three clamped edges and one free edge under uniformly distributed load is found by RTM: finally, we analyze numerical results of the solution.
TL;DR: Based on the microscopic mechanism of the rotational plastic deformation, the conservation equation satisfied by the defects motion (dislocation and disclination) has been developed in this article, where the diffusion motion of the defects are reduced based on the asymmetric theory of continuum mechanics.
Abstract: Experiments have shown the strong rotation in plastic deformation, which is caused by the disclination, specific arrangement of dislocation and inhomogeneity of the gliding motion of the defects in the microscopic scale. Based on the microscopic mechanism of the rotational plastic deformation, the conservation equation satisfied by the defects motion (dislocation and disclination) has been developed in this paper. Then the diffusion motion of the defects are reduced based on the asymmetric theory of continuum mechanics. By utilizing the maximization procedure for the micro plastic work and a scale-invariance argument, various models of Cosserat-type plasticity are obtained in this manner.
TL;DR: In this article, an exact solution on the stress distribution of fillet welds is obtained, which can be used not only for estimating the accuracy of the present design method, but also for establishing a new design method.
Abstract: An exact solution on the stress distribution of fillet welds is obtained in this paper. This solution can be used not only for estimating the accuracy of the present design method of fillet welds but also for establishing a new design method.
TL;DR: In this article, the relation between the dynamics on the base space of a vector bundle and that on each associated bundle of frames is discussed and a continuation of a previous one is presented.
Abstract: This paper is a continuation of a previous one. We still emphasize the discussion on the relation between the dynamics on the base space of a vector bundle and that on each associated bundle of frames.
TL;DR: By using the basic displacements and stresses caused by a single elastic inclusion and a single crack on infinite plane, the interaction problem between a crack and an elastic inclusion is reduced to solve a set of Cauchy-type singular integral equation as discussed by the authors.
Abstract: By using the basic displacements and stresses caused by a single elastic inclusion and a single crack on infinite plane, the interaction problem between a crack and an elastic inclusion is reduced to solve a set of Cauchy-type singular integral equation. Based on this result, the singular behaviour of the solution for the inclusion-branching crack is analysed theoretically and the oscillating singular interface stress field is obtained. For the separating inclusion-crack problem, the stress intensity factors at the tips and the interface stress of the inclusion are calculated and the results of which are satisfactory.
TL;DR: In this article, the displacement and stress distributions in a spherically isotropic cone subjected to concentrated loads at apex are studied and the hollow cone problems are discussed, based on the Ref.
Abstract: Based on the Ref. [9], the displacement and stress distributions in a spherically isotropic cone subjected to concentrated loads at apex are studied. The displacement and stresses are given explicily for the cone in compression torsion and bending cases, respectively, based on the situation of the concentrated forces and moments. Finally, the hollow cone problems are discussed.
TL;DR: In this paper, it was shown that any 3D dynamical system of ODEs with time-independent invariants can be rewritten as Hamiltonian systems with respect to generalized Poisson brackets and the Hamiltonians are these invariants.
Abstract: We have proved that any 3-dimensional dynamical system of ordinary differential equations (in short, 3D ODE) with time-independent invariants can be rewritten as Hamiltonian systems with respect to generalized Poisson brackets and the Hamiltonians are these invariants. As an example, we discuss the Kermack-Mckendrick model for epidemics in detail. The results we obtained are generalization of those obtained by Y. Nutku.
TL;DR: In this paper, the static response and reliability of uncertain structures with vector-valued and matrix-valued functions was studied. But the static responses were not analyzed for the case of the random variables and system derivatives, and generalized mathematical formulae for probabilistic perturbation were obtained.
Abstract: This paper studies the static response and reliability of uncertain structures with vector-valued and matrix-valued functions. The finite element analysis method of uncertain structures is based on matrix calculus, Kronecker algebra and perturbation theory. Random variables and system derivatives are conveniently arranged into 2D matrices and generalized mathematical formulae for probabilistic perturbation are obtained.
TL;DR: In this paper, the momentum of a free particle motion with high-level speed presenting nonlinear effects was expanded by using Laurent series and then obtained the complete expression of nonlinear and unsteady momentum.
Abstract: In this paper we consider that the momentum of a free particle motion with high-level speed presenting nonlinear effects may be expanded by using Laurent series and then obtain the complete expression of nonlinear and unsteady momentum. These nonlinear and unsteady phenomena of high-level speed may further expand to the theory of kinematics and it may be determined by Fredholm's integral equation of the first kind. In addition, according to the nonlinear and unsteady momentum obtained the relations of the nonlinear mechanics equations, work and energy, mass and energy may be derived. Finally, this paper also calculates those experimental results which done in particle physics for mu-mesons u± and fast neutrons n, these results are in agreement with data perfectly.
TL;DR: In this article, two types of similarity reductions of the super KdV equation are given by the direct method, and they are shown to be equivalent to the direct reduction of the K-means equation.
Abstract: In this paper, two types of similarity reductions of the super KdV equation are given by the direct method
TL;DR: In this paper, the authors analyzed the blood-mechanical heart valve interaction system subjected to a step pressure when the value is, at closing position, and demonstrated that in such conditions mechanical values made of pyrolytic carbon, Ti alloy, Co-Cr alloy and ceramics tend to be very stiff which result in high impinging pressure.
Abstract: Using finite element method, this paper has analyzed the blood-mechanical heart valve interaction system subjected to a step pressure when the value is, at closing position. As demonstrated in the present study, in, such conditions mechanical values made of pyrolytic carbon, Ti alloy, Co-Cr alloy and ceramics tend to be very stiff which result in high impinging pressure. The impinging pressure acted on the value of the blood-valve system can be reduced by decreasing the elastic modulus of the mechanical value.
TL;DR: In this article, the authors investigated the Ishikawa iteration process in a p-uniformly smooth Banach space X and showed that sol(T) is a singleton.
Abstract: In this paper, we investigate the Ishikawa iteration process in a p-uniformly smooth Banach space X. Let T: X→X be a Lipschitzian and local strongly accretive operator and the set sol(T) of solutions of the equation Tx=f be nonempty. We show that sol(T) is a singleton and the Ishikawa sequence converges strongly to the unique solution of the equation Tx=f. In addition, whenever T is a Lipschitzian and local pseudocontractive mapping from a nonempty convex subset K of X and the set F(T) of fixed points of T is nonempty, we prove that F(T) is a singleton and the Ishikawa sequence converges strongly to the unique fixed point of T. Our results are the improvements and extension of the results of Deng and Ding(4) and Tan and Xu(5).
TL;DR: In this paper, a class of parallel, multisplitting accelerated overrelaxation (AOR) method is set up for solving large-scale system of nonlinear algebraic equations Aϕ(x)+Bψ(x)=b.
Abstract: A class of parallel, multisplitting accelerated overrelaxation (AOR) method is set up for solving large-scale system of nonlinear algebraic equations Aϕ(x)+Bψ(x)=b. Under certain conditions, we prove the existence and uniqueness of the solution of this system of nonlinear equations and set up the global convergence theory of the new method.
TL;DR: By the improvement of Riks' and Crisfield's arc-length method, the adaptive parameter incremental method is prensted for predicting the snapping response of structures and its justification is fulfilled.
Abstract: By the improvement of Riks' and Crisfield's arc-length method, the adaptive parameter incremental method is prensted for predicting the snapping response of structures. Its justification is fulfilled. Finally, the effectiveness of this method is demonstrated by solving the snapping response of spherical caps subjected to centrally distributed pressures.
TL;DR: In this paper, the post-buckling of a simply supported column with a solid rectangular cross-section is analyzed by a new approach, where high order terms in the asymptotic postbuckling expansions are carried out.
Abstract: The plastic post-buckling of a simply supported column with a solid rectangular cross-section is analysed by a new approach. High order terms in the asymptotic postbuckling expansions are carried out. In some aspects, the method proposed in this paper is similar to Hutchinson's. However, the computation is simple since the introduction is avoided of stretched coordinates. The method can be used to analyse initial post-bifurcation of plates and shells in the plastic range.
TL;DR: In this paper, the authors prove that the turbulence closure problem is caused by lack of statistical distribution in present turbulence theory, and the restriction of turbulence model theory and the shortcoming of direct numerical simulation of N-S to solve the turbulence have been pointed out.
Abstract: It is a wrong viewpoint that the turbulence closure problem is due to the non-linearity of N-S equation, because if we omit the non-linear terms in N-S equation, many physical quantities can not be obtained other than the mean-values. In this paper, we proof that the closure problem of turbulence be induced by lack of statistical distribution in present turbulence theory. And the restriction of turbulence model theory and shortcoming of direct numerical simulation of N-S to solve the turbulence have been pointed out.
TL;DR: Based on the general theory of elastic plates which abandons Kirchhoff-love assumption in the classical theory, this article established a first order approximation theory for elastic circular plates with non-Kirchhoff Love assumption, and presented an analytic solution to the axisymmetric problem of elastic circular plate with clamped boundary under uniformly distributed load.
Abstract: Based on the general theory of elastic plates which abandons Kirchhoff-Love assumption in the classical theory, this paper establishes a first order approximation theory of elastic circular plates with non-Kirchhoff-Love assumption, and presents an analytic solution to the axisymmetric problem of elastic circular plates with clamped boundary under uniformly distributed load. By comparing with the classical solution of the thin circular plates, it is verified that the new solution is closer to the experiment results than the classical solution. By virtue of the new theory, the influence of the diameter-to-thickness ratio upon the precision of the classical theory is examined.
TL;DR: In this article, the obsolute stability for zero solution of the discrete type Lurie control system was discussed and necessary and sufficient conditions for the absolute stability for system (1) under conditions (2) and sufficient criteria for absolute stability of the simplified system of system (3).
Abstract: In this paper, it is discussed that the obsolute stability for zero solution of the discrete type Lurie control system
(1)
$$\left. {\begin{array}{*{20}c} {x(n + 1) = Ax(n) + bf[\sigma (n)]} \\ {\sigma (n) = c^T x(n)} \\ \end{array} } \right\}$$
in which the nonlinear function f(δ) satisfying conditions as follows
(2)
$$\begin{array}{*{20}c} {f(0) = 0,\sigma f(\sigma ) > 0} & {(\sigma
e 0)} \\ \end{array}$$
or
(3)
$$\begin{array}{*{20}c} {f(0) = 0,0 \leqslant k_1 \leqslant f(\sigma )/\sigma \leqslant k_2< + \infty } & {(\sigma
e 0)} \\ \end{array}$$
It gives the necessary and sufficient conditions for the absolute stability for system (1) under conditions (2). We also obtain the sufficient criteria for absolute stability of the simplified system of (1) under conditions (3).
TL;DR: In this paper, an interface crack analysis is presented for further understanding the characteristics of the crack-tip field, and a closed-form solution for stress intensity factors in terms of external loading as well as geometric and material parameters for fairly general composite laminates is derived.
Abstract: An interface crack analysis is presented for further understanding the characteristics of the crack-tip field. The conditions under which the energy release rate components would exist are emphasized, and the relations between energy release rate components and the stress intensity factors are given. Combining with the results of classical plate theory analysis, a closed-form solution for stress intensity factors in terms of external loading as well as some geometric and material parameters for fairly general composite laminates is derived. Then, an analytical solution for energy release rate components is deduced. In order to get energy release rate components under general loading condition, a mode mix parameter, Ω, must be determined separately. A methodology for determining Ω is discussed. Finally, several different kinds of laminates are exmained, and the results obtained could be used in engineering applications.