Showing papers in "Applied Mathematics and Mechanics-english Edition in 1989"
TL;DR: In this article, it was shown that if T is a mapping of a closed convex nonempty subset K of a convex metric space into itself satisfying the inequality, then T has a unique fixed point in K.
Abstract: Let X be a convex metric space with the property that even decreasing sequence of nonempty closed subsets of X with diameters tending to zero has nonempty intersection This paper proved that if T is a mapping of a closed convex nonempty subset K of X into itself satisfying the inequality: d(Tx, Ty)⩽ad(x, y)+b{d(x, Tx)+d(y, Ty)} +c{d(x, Ty)+d(y, Tx)} for all x, y in K, where 0⩽a<1, b⩾0, c⩾0, a+c≠0 and a+2b+3c⩽1, then T has a unique fixed point in K.
45 citations
TL;DR: In this article, a Fourier pseudo-spectral method with a restraint operator for the SRLW equation is presented, and the stability of the schemes and optimum error estimates are given.
Abstract: In this paper we present a Fourier pseudo-spectral method with a restraint operator for the SRLW equation. We prove the stability of the schemes and give optimum error estimates.
22 citations
TL;DR: In this paper, the Leray-Schauder topological degree theory in the probabilistic linear normed spaces is established and fixed point theorems for mappings in the space are shown.
Abstract: The Leray-Schauder topological degree theory is established in the probabilistic linear normed spaces. Based on this theory, some fixed point theorems for mappings in the probabilistic linear normed spaces are shown.
18 citations
TL;DR: In this paper, the equivalence between Ekeland's variational principle and Caristi's fixed point theorem has been proved by using a simple method, and the results stated in this paper improve and strengthen the corresponding results in [4].
Abstract: This paper proposes a formally stronger set-valued Caristi's fixed point theorem and by using a simple method we give a direct proof for the equivalence between Ekeland's variational principle and this set-valued Caristi's fixed point theorem. The results stated in this paper improve and strengthen the corresponding results in [4].
16 citations
TL;DR: In this paper, a quasilinear second order ordinary differential equation with a small parameter is considered and an appropriate problem is constructed, and an iterative procedure is developed.
Abstract: In this paper we consider a quasilinear second order ordinary differential equation with a small parameter e. Firstly an appropriate problem is constructed. Then an iterative procedure is developed. Finally we give an algorithm whose accuracy is good for arbitrary e>0.
11 citations
TL;DR: In this article, analytical solutions to the partial differential equations for unsteady flow of second-order fluid and Maxwell fluid in tube by using the integral transform method were presented, which can be used to analyse the behaviour of axial velocity and shear stress for non-Newtonian visco-elastic fluids in tube, and to provide a theoretical base for the projection of pipe-line engineering.
Abstract: This paper presents analytical solutions to the partial differential equations for unsteady flow of the second-order fluid and Maxwell fluid in tube by using the integral transform method. It can be used to analyse the behaviour of axial velocity and shear stress for unsteady flow of non-Newtonian visco-elastic fluids in tube, and to provide a theoretical base for the projection of pipe-line engineering.
9 citations
TL;DR: In this article, the method of the reciprocal theorem (MRT) is extended to solve the steady state responses of rectangular plates under harmonic disturbing forces and a series of closed solutions of rectangular plate with various boundary conditions are given and the tables and figures which have practical value are provided.
Abstract: In this paper the method of the reciprocal theorem (MRT) is extended to solve the steady state responses of rectangular plates under harmonic disturbing forces. A series of the closed solutions of rectangular plates with various boundary conditions are given and the tables and figures which have practical value are provided.
9 citations
TL;DR: In this article, the large deflection theory is adopted to analyse the geometrical nonlinear stability of a sandwich shallow cylindrical panel with orthotropic surfaces, and the critical point is determined and the postbuckling behaviour of the panel is studied.
Abstract: In this paper, the large deflection theory is adopted to analyse the geometrical nonlinear stability of a sandwich shallow cylindrical panel with orthotropic surfaces. The critical point is determined and the postbuckling behaviour of the panel is studied.
8 citations
TL;DR: In this article, the postbuckling behavior of simply supported rectangular orthotropic plates under inplane compression is investigated, and two types of in-plane boundary conditions are considered and the effects of initial imperfections are also studied.
Abstract: In this paper, applying perturbation method to von Karman-type nonlinear large deflection equations of orthotropic plates by taking deflection as perturbation parameter, the postbuckling behavior of simply supported rectangular orthotropic plates under inplane compression is investigated. Two types of in-plane boundary conditions are now considered and the effects of initial imperfections are also studied. Numerical results are presented for various cases of orthotropic composite plates having different elastic properties. It is found that the results obtained are in good agreement with those of experiments.
8 citations
TL;DR: In this paper, a nonlinear solution for a circular sandwich plate with the flexure rigidity of the face layers taken into account is presented. And the results are compared with those from Liu Ren-huai and Shi-Yun-fang.
Abstract: In this paper, a nonlinear solution is first presented for a circular sandwich plate with the flexure rigidity of the face layers taken into account. In solving the nonlinear bending equations, a modified power series method is proposed. The uniformly distributed loading and the clamped but sliding boundary condition are also assumed. Then our results are compared with those from Liu Ren-huai and Shi-Yun-fang[15]. The present solution can be used as a more accurate basis in engineering applications.
8 citations
TL;DR: In this article, the exact analytic method is suggested to solve variable coefficient differential equations under arbitrary boundary condition, and the general computation format is obtained by this method, and its convergence is proved.
Abstract: Many engineering problems can be reduced to the solution of a variable coefficient differential equation. In this paper, the exact analytic method is suggested to solve variable coefficient differential equations under arbitrary boundary condition. By this method, the general computation format is obtained. Its convergence is proved. We can get analytic expressions which converge to exact solution and its higher order derivatives unifornuy. Four numerical examples are given, which indicate that satisfactory results can be obtained by this method.
TL;DR: In this paper, the bending problem of rectangular thin plates with free edges laid on tensionless Winkler foundation has been solved by employing Fourier series with supplementary terms, assuming proper form of series for deflection, the basic differential equation with given boundary conditions can be transformed into a set of infinite algebraic equations.
Abstract: In this paper, the bending problem of rectangular thin plates with free edges laid on tensionless Winkler foundation has been solved by employing Fourier series with supplementary terms. By assuming proper form of series for deflection, the basic differential equation with given boundary conditions can be transformed into a set of infinite algebraic equations. Because the boundary of contact region cannot be determined in advance, these equations are weak nonlinear ones. They can be solved by using iterative procedures.
TL;DR: In this paper, the authors give necessary and sufficient conditions for absolute stability of several classes of direct control systems, and discuss the relative stability of the first canonical form of control system, which they call direct control system.
Abstract: In this paper, we give necessary and sufficient conditions for absolute stability of several classes of direct control systems, and discuss the absolute stability of the first canonical form of control system. The corresponding results in references [3,5,6] and [7] are improved.
TL;DR: In this article, a stress deformation constitutive relation expressed by functional tensorial expression is found for anisotropic damage in a macroscopic continuum mechanics model and a microdefect model.
Abstract: In this paper, the stress deformation constitutive relations for continua are discussed and a stress deformation constitutive relation expressed by functional tensorial expression is found. When we study the anisotropic damage of anisotropic materials either from a macroscopic continuum mechanics model or from a microdefect model, there exists a limit to the order of a damage tensor, and the condition under which the damage variable may be described by a tensor lower than those of the highest order is found.
TL;DR: In this article, the objective stress rate in co-moving coordinate is derived by applying nonlinear geometric field theory of deformation, which is a rather important problem in mechanics of finite deformation.
Abstract: The objective stress rate is a rather important problem in mechanics of finite deformation. In this paper, the objective stress rate in co-moving coordinate is derived by applying nonlinear geometric field theory of deformation. Problems, such as large extension coupled with rotation, and large shear deformation, are exemplified by using the new formula. Comparing with Jaumann's stress rate and other formulae presented in current literature, the new result appears to be the reasonable one in co-moving coordinate system.
TL;DR: In this article, a numerical solution of hyperbolic cooling tower shell, a class of full nonlinear problems in solid mechanics of considerable interest in engineering applications, is presented. But the authors focus on the postbuckling analysis of cooling tower shells with discrete fixed support under the action of wind loads and dead load.
Abstract: This paper is concerned with a numerical solution of hyperbolic cooling tower shell, a class of full nonlinear problems in solid mechanics of considerable interest in engineering applications. In this analysis, the post-buckling analysis of cooling tower shell with discrete fixed support and under the action of wind loads and dead load is studied. The influences of ring-stiffener on instability load are also discussed. In addition, a new solution procedure for nonlinear problems which is the combination of load increment iteration with modified R-C are- length method is suggested. Finally, some conclusions having important significance for practice engineering are given.
TL;DR: In this article, the authors enumerated weighted lattice paths by counting function, which is a natural extension of Gaussian multinomial coefficient in the case of unrestricted paths, which yields some Vandermunde-type identities for multiinomial and q-multinomial coefficients.
Abstract: An independent method for paper [10]is presented. Weighted lattice paths are enumerated by counting function which is a natural extension of Gaussian multinomial coefficient in the case of unrestricted paths. Convolutions for path counts are investigated, which yields some Vandermunde-type identities for multinomial and q — multinomial coefficients.
TL;DR: In this article, some misunderstandings concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of necessary conditions has been offered.
Abstract: In this paper, some misunderstandings concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of necessary conditions for resonance has been offered.
TL;DR: In this paper, a uniform analysis of the asymptotic properties of high frequencies of non-uniform bars, beams and circular membranes is given by using perturbation method, and the case of discontinuous physical parameters is also discussed.
Abstract: In this paper, a uniform analysis of the asymptotic properties of high frequencies of non-uniform bars, beams and circular membranes is given by using perturbation method, and the case of discontinuous physical parameters is also discussed.
TL;DR: In this article, a hydrodynamic stability theory of distorted laminar flow is proposed and a kind of distortion profile of mean velocity in parallel shear flow has been presented.
Abstract: This paper suggests a hydrodynamic stability theory of distorted laminar flow, and presents a kind of distortion profile of mean velocity in parallel shear flow. With such distortion profiles, the new theory can be used to investigate the stability behaviour of parallel shear flow, and thus suggests a new possible approach to instability.
TL;DR: In this article, the collapse of a vaporous bubble in an incompressible liquid with surface tension was analyzed using Rayleigh's method, and expressions of time versus radius, bubble-wall velocity and pressure developed at collapse were introduced.
Abstract: Employing Rayleigh's method, the collapse of a vaporous bubble in an incompressible liquid with surface tension is analysed. The expressions of time versus radius, bubble-wall velocity and pressure developed at collapse are thus introduced.
TL;DR: In this paper, classical linear elastic variational principles are derived from the reciprocal theorem and mixed variational principle of variations of boundary conditions are given, which are then systematically derived from a linear variational framework.
Abstract: In this paper classical linear elastic variational principles are systematically derived from the reciprocal theorem and mixed variational principles of variations of boundary conditions are given.
TL;DR: In this article, the shape functions of the finite annular plate element were used as shape functions and some integration difficulties related to the Bessel's functions were solved in the context of structural characteristic analysis and dynamic response computation.
Abstract: The dynamic deformation of harmonic vibration is used as the shape functions of the finite annular plate element, and some integration difficulties related to the Bessel's functions are solved in this paper. Then the dynamic stiffness matrix of the finite annular plate element is established in closed form and checked by the direct stiffness method. The paper has given wide converage for decomposing the dynamic matrix into the power series of frequency square. By utilizing the axial symmetry of annular elements, the modes with different numbers of nodal diameters are separately treated. Thus some terse and complete results are obtained as the foundation of structural characteristic analysis and dynamic response computation.
TL;DR: Based on the nonlinear large deflection equations of von Karman plates, the lateral pressure was first converted into an initial deflection by Galerkin method, the postbuckling behavior of simply supported rectangular plates under uniaxial compression combined with lateral pressure is then studied applying perturbation method by taking deflection as perturbance parameter as discussed by the authors.
Abstract: Based on the nonlinear large deflection equations of von Karman plates, the lateral pressure is first converted into an initial deflection by Galerkin method, the postbuckling behavior of simply supported rectangular plates under uniaxial compression combined with lateral pressure is then studied applying perturbation method by taking deflection as perturbation parameter.
TL;DR: In this paper, the method of differential inequalities has been applied to study the boundary value problems of nonlinear ordinary differential equation with two parameters, and the asymptotic solutions have been found and the remainders have been estimated.
Abstract: In this paper, the method of differential inequalities has been applied to study the boundary value problems of nonlinear ordinary differential equation with two parameters. The asymptotic solutions have been found and the remainders have been estimated.
TL;DR: In this article, the growth, equilibrium and stabilization of free gas nucleus are analyzed and it is shown that the cavitation results from the growth of Free Gas nucleus to critical radius and conditions of cavitation have been derived.
Abstract: The growth, equilibrium and stabilization of free gas nucleus are analyzed. It is shown that the cavitation results from growth of free gas nucleus to critical radius and conditions of cavitation have been derived.
TL;DR: In this article, the reaction forces of elastical supports at points are regarded as unknown external forces acting on the membranes, and the exact solution of the equation of motion is given which includes terms representing the unknown reaction forces.
Abstract: This paper presents a new method for solving the vibration of arbitrarily shaped membranes with elastical supports at points. The reaction forces of elastical supports at points are regarded as unknown external forces acting on the membranes. The exact solution of the equation of motion is given which includes terms representing the unknown reaction forces. The frequency equation is derived by the use of the linear relationship of the displacements with the reaction forces of elastical supports at points. Finally the calculating formulae of the frequency equation of circular membranes are analytically performed as examples and the inherent frequencies of circular membranes with symmetric elastical supports at two points are numerically calculated.
TL;DR: In this paper, the method of approximate compulation for the lowest eigenfrequencies of rectangular plates, on which there are symmetrical concentrated masses, supported at corner points, is discussed.
Abstract: This paper discusses by energy Theorem the method of approximate compulation for the lowest eigenfrequcncies of rectangular plates, on which there are symmetrical concentrated masses, supported at corner points. In the case of several concentrated masses, by using the principle of superposition we may find the reduced coefficients of masses conveniently. Hence we can obtain the lowest eigenfrequencies of thin plates. In the paper a good many numerical calculating examples are illustrated.
TL;DR: In this paper, the authors employed the diagonalization technique to transform a vector second-order nonlinear system into two first-order approximate diagonalized systems and obtained the existence and the asymptotic behavior of the solutions.
Abstract: In this paper the method and technique of the diagonalization are employed to transform a vector second-order nonlinear system into two first-order approximate diagonalized systems. The existence and the asymptotic behavior of the solutions are obtained for a vector second-order nonlinear Robin problem of singular perturbation type.
TL;DR: In this article, the authors give the theorems concerning the summation of trigonometric series with the help of Fourier transforms, by means of the known results of the Fourier transform.
Abstract: This paper gives the theorems concerning the summation of trigonometric series with the help of Fourier transforms. By means of the known results of Fourier transforms, many difficult and complex problems of summation of trigonometric series can be solved. This method is a comparatively unusual way to find the summation of trigonometric series, and has been used to establish the comprehensive table of summation of trigonometric series. In this table 10 thousand series are given and most of them are new.