Showing papers in "Applied Mathematics and Mechanics-english Edition in 1991"
TL;DR: In this paper, some existence theorems of common and coincidence solutions for a class of more general systems of functional equations arising in dynamic programming are shown, and the results contain the corresponding results of [6,7] as special cases.
Abstract: Some existence theorems of common and coincidence solutions for a class of more general systems of functional equations arising in dynamic programming are shown. The results presented in this paper not only contain the corresponding results of [6,7] as special cases, but also give an existence theorem of solutions for a class of functional equations suggested by Wang[2–5] recently.
27 citations
TL;DR: In this article, a theoretical analysis for the stability of laminated composite circular conical shells under external pressure is presented based on the mixed-type theory developed by the same authors.
Abstract: In this paper, based on the mixed-type theory developed by the same authors[1], a theoretical analysis is presented for the stability of laminated composite circular conical shells under external pressure. The formulas for critical external pressure are obtained by using the potential energy variation principle. Very good agreement is shown between the theoretical prediction of critical external pressure and the experimental data. Finally, the influence of some parameters on critical external pressure is discussed numerically. The mixed-type theory developed by the same authors[1] and the results obtained in this paper are very useful in aerospace engineering design.
22 citations
TL;DR: In this article, the concept of e-chainable PM-space is introduced, and several fixed point theorems of one-valued and multivalued local contraction mapping on the kind of spaces are given.
Abstract: In this paper, we introduce the concept of e-chainablePM-space, and give several fixed point theorems of one-valued and multivalued local contraction mapping on the kind of spaces.
19 citations
TL;DR: In this paper, the variational principles of Jourdain's form of nonlinear nonholonomic nonpotential system in noninertial reference frame are established, the generalized Noether's theorem of the system above is presented and proved, and the conserved quantities of system are studied.
Abstract: The new Lagrangian of the relative motion of mechanical system is constructed, the variational principles of Jourdain's form of nonlinear nonholonomic nonpotential system in noninertial reference frame are established, the generalized Noether's theorem of the system above is presented and proved, and the conserved quantities of system are studied.
19 citations
TL;DR: In this paper, the thermalbuckling of thin annular plates subjected to a field of non-uniform axisymmetric temperature and a variety of boundary conditions is discussed.
Abstract: On the basis of Von Karman equations, the thermal-buckling of thin annular plates subjected to a field of non-uniform axisymmetric temperature and a variety of boundary conditions is discussed. The linearized problem is analyzed and stability boundaries which characterize instability of a plate are obtained by means of numerical and analysis methods.
14 citations
TL;DR: In this paper, a quasi-variational inequality is proved in paracompact setting which generalizes the results of Zhou Chen and Aubin and two existence theorems on the solutions of optimization problems and social equilibria of metagames are showed.
Abstract: A quasi-variational inequality is proved in paracompact setting which generalizes the results of Zhou Chen and Aubin. As applications, two existence theorems on the solutions of optimization problems and social equilibria of metagames are showed which improve and extend the recent results of Kaczynski-Zeidan and Aubin.
13 citations
TL;DR: In this paper, the authors make detailed analyses for the flexural vibration (frequency) of the hemispherical shell and present the varying laws of frequency with the varying boundary angles and the wall thickness of the above shell.
Abstract: This paper makes detailed analyses for the flexural vibration (frequency) of the hemispherical shell and presents the varying laws of frequency with the varying boundary angles and the wall thickness of the above shell. It is an important value to develop the instrument, such as hemispherical resonator gyro (HRG), whose sensing component is a hemispherical shell.
13 citations
TL;DR: In this article, the boundary layer theory for the buckling of thin alastic shells suggested in ref. [1] was used to analyze the postbuckling behavior of stiffened cylindrical shells.
Abstract: Buckling and postbuckling behaviors of perfect and imperfect, stringer and orthotropically stiffened cylindrical shells have been studied under axial compression. Based on the boundary layer theory for the buckling of thin alastic shells suggested in ref. [1], a theoretical analysis is presented. The effects of material properties of stiffeners and skin, which are made of different materials, on the buckling load and postbuckling behavior of stiffened cylindrical shells have also been discussed.
12 citations
TL;DR: In this article, the effect of the angle of inclination of the concentrated force upon the deformed shape, the load-deflection relationship and the length of the plastic region was analyzed.
Abstract: Based on the Plastica theory (see ref. [12]), the large deflection of an elastic-perfectly plastic cantilever subjected to an inclined concentrated force at its tip, before the unloading in the plastic region occurs, is analyzed in this paper. The emphasis of the analysis is put on the effects of the angle of inclination of the concentrated force upon the deformed shape, the load-deflection relationship and the length of the plastic region. Both analytical and computed results are given.
12 citations
TL;DR: In this paper, some thermoelastic problems in the half space are studied by using the general solutions of the elastic equations, and the method presented here is extremely effective for the axisymmetric problems of the half-space as well as the half plane problems.
Abstract: In this paper, some thermoelastic problems in the half space are studied by using the general solutions of the elastic equations. The method presented here is extremely effective for the axisymmetric problems of the half space as well as the half plane problems.
10 citations
TL;DR: In this paper, the general equations of dynamic stability for composite laminated plates are derived by Hamilton principle and the solutions of the fundamental equations show that some important characteristics of the dynamic instability can only be got by the consideration and analysis of those factors.
Abstract: In this paper, the general equations of dynamic stability for composite laminated plates are derived by Hamilton principle. These general equations can be used to consider those different factors that affect the dynamic stability of laminated plates. The factors are transverse shear deformation, initial imperfections, longitudinal and rotational inertia, and ply-angle of the fiber, etc. The solutions of the fundamental equations show that some important characteristics of the dynamic instability can only be got by the consideration and analysis of those factors.
TL;DR: In this article, the degeneration of the eigenvalue equation of the discrete-time linear quadratic control problem to the continuous-time one when Δt→0 is given first.
Abstract: The degeneration of the eigenvalue equation of the discrete-time linear quadratic control problem to the continuous-time one when Δt→0 is given first. When the continuous-time n-dimensional eigenvalue equation, which has all the eigenvalues located in the left half plane, has beeh reduced from the original 2n-dimensional one, the present paper proposes that several of the eigenvalues nearest to the imaginary axis be obtained by the matrix transformation Ae=eA. All the eigenvalues of Ae are in the unit circle, with the eigenvectors unchanged and the original eigenvalues can be obtained by a logarithm operation. And several of the eigenvalues of Ae nearest to the unit circle can be calculated by the dual subspace iteration method.
TL;DR: In this article, a non-isotropic multiple-scale turbulence model (MS/ASM) is proposed for complex flow calculations, which focuses on the direct modeling of Reynolds stresses and utilizes split-spectrum concepts to model multiplescale effects in turbulence.
Abstract: This paper describes a newly developed non-isotropic multiple-scale turbulence model (MS/ASM) for complex flow calculations. This model focuses on the direct modeling of Reynolds stresses and utilizes split-spectrum concepts to model multiple-scale effects in turbulence. Validation studies on free shear flows, rotating flows and recirculating flows show that the current model performs significantly better than the single-scalek−e model. The present model is relatively inexpensive in terms of CPU time which makes in suitable for broad engineering flow applications.
TL;DR: In this article, the large deflection theory of symmetrically laminated cylindrically orthotropic shallow spherical shells is established, and the analytic solution for critical buckling loads of the shells with rigidly clamped edges under actions of uniform pressure has been obtained.
Abstract: In this paper, the large deflection theory of symmetrically laminated cylindrically orthotropic shallow spherical shells is established. Based on this theory, applying the modified iteration method, the analytic solution for critical buckling loads of the shells with rigidly clamped edges under actions of uniform pressure has been obtained.
TL;DR: In this article, by the property of conjugate operator, the authors give a method to construct the general solutions of a system of partial differential equations, which is not only theoretical significance, but also practical value.
Abstract: Solving partial differential equations was not only theoretical significance, but also practical value. In this paper, by the property of conjugate operator, we give a method to construct the general solutions of a system of partial differential equations.
TL;DR: Based on the situation of welding thermal conduction and thermo-elasto-plastity research, the authors explores some problems in this field and provides a comparison of calculated results with experimental data.
Abstract: Based on the situation of welding thermal conduction and thermo-elasto-plastity research, this paper explores some problems in this field. First, the Boundary Element Method for non-linear problems is improved by linearization of non-linear problems and used in welding thermal conduction analysis. Second, the thermo-elasto-plastic Finite Element Method is used for the welding stress calculation, in which, the phase transformation is considered by the “equivalent linear expansion coefficient method”. The comparison of calculated results with experimental data shows that the methods provided in this paper are available.
TL;DR: In this paper, the exact integral equation of Hertz's contact problem was obtained by taking into account the horizontal displacement of points in the contacted surfaces due to pressure, which is obtained by assuming that the contact surfaces are smooth.
Abstract: This paper presents the exact integral equation of Hertz's contact problem, which is obtained by taking into account the horizontal displacement of points in the contacted surfaces due to pressure.
TL;DR: In this article, the displacements and body-forces are resolved, respectively, and the 3D equilibrium problems of spherically isotropic bodies with body forces are transferred into a two-order differential equation and a four-order equation.
Abstract: In this paper the displacements and body-forces are resolved, respectively, and the 3-dimensional equilibrium problems of spherically isotropic bodies with body-forces are transferred into a two-order differential equation and a four-order differential equation. Based on the series expansion technique and properties of spherical functions, the series solutions are obtained for the corresponding homogeneous equations, which can be adapted to solve equilibrium problems of whole spheres or spherical shells. The special solution for a revolving sphere is also given.
TL;DR: In this paper, a second order linear ordinary differential equation with n-turning points was studied, where q1(x)=(x-μ1) (x-m) f(x), f (x)≠0, and λ is a large parameter.
Abstract: This paper studies a second order linear ordinary differential equation with n-turning points
$$\frac{{d^2 y}}{{dx^2 }} + [\lambda ^2 q_1 (x) + q_2 (x)]y = 0$$
Where q1(x)=(x-μ1) (x-μ2) ... (x-μm) f(x), f(x)≠0, and λ is a large parameter.
TL;DR: In this paper, a new unified and general class of variational inequalities is introduced, and the existence and uniqueness results of solutions for this kind of inequalities are presented. And the results presented in this paper are applied to the Signorini problem in mechanics.
Abstract: In this paper, we introduce a new unified and general class of variational inequalities, and show some existence and uniqueness results of solutions for this kind of variational inequalities. As an application, we utilize the results presented in this paper to study the Signorini problem in mechanics.
TL;DR: In this paper, the finite element equation for the spherical shell was established and the resonant frequencies of the above shell under different boundary conditions were discussed and calculated, and the exact resonant frequency was also discussed.
Abstract: This paper establishes the finite element equation for the spherical shell. The resonant frequencies of the above shell under different boundary conditions are also discussed and calculated.
TL;DR: In this paper, the numerical solution of a singularly perturbed problem for the quasilinear parabolic differential equation was considered and a linear three-level finite difference scheme on a nonuniform grid was constructed.
Abstract: We consider the numerical solution of a singularly perturbed problem for the quasilinear parabolic differential equation, and construct a linear three-level finite difference scheme on a nonuniform grid. The uniform convergence in the sense of discrete L2 norm is proved and numerical examples are presented.
TL;DR: In this paper, the iterative approximation of the solution of nonlinear equation Tx=y is given and the iteration of a fixed point of a locally Lipschitzian and strictly pseudo-contractive mapping is discussed.
Abstract: Suppose X=Lp (orlp),p>2, T:D(T)→X is a locally Lipschitzian and strictly accretive operator. In this paper, the iterative approximation of the solution of nonlinear equation Tx=y is given and the iterative approximation of a fixed point of a locally Lipschitzian and strictly pseudo-contractive mapping is discussed.
TL;DR: In this paper, the authors introduced the concept of probabilistic contractor couples in non-Archimedean probabilistically normed spaces and studied the existence and uniqueness of solutions for a system of nonlinear operator equations with Probabilistic Contractor Couples.
Abstract: The Purpose of this paper is to introduce the concept of probabilistic contractor couple in non-Archimedean probabilistic normed spaces and to study the existence and uniqueness of solutions for a system of nonlinear operator equations with probabilistic contractor couples in non-Archimedean probabilistic normed spaces. The results presented in this paper improve and extend the corresponding results in [1–5].
TL;DR: In this article, a generalized form of the method of full approximation is presented, where the original nonlinear problems are linearized and their higher-order solutions are given in terms of the first-term asymptotic solutions and corresponding transformations.
Abstract: This paper presents a generalized form of the method of full approximation. By using the concept of asymptotic linearization and making the coordinate transformations including the nonlinear functionals of dependent variables, the original nonlinear problems are linearized and their higher-order solutions are given in terms of the first-term asymptotic solutions and corresponding transformations. The analysis of a model equation and some problems of weakly nonlinear oscillations and waves with the generalized method shows that it is effective and straightforward.
TL;DR: In this article, a class of singularly perturbed initial-boundary value problems for the reaction diffusion systems is considered, and it is shown that these problems have a solution and obtain their asymptotic expansion.
Abstract: In this paper, a class of singularly perturbed initial-boundary value problems for the reaction diffusion systems is considered. Using the theory of differential inequality, we prove that the initial-boundary value problems have a solution and obtain their asymptotic expansion.
TL;DR: In this paper, the velocity potentials of singularities moving with an arbitrary path either in the upper fluid or in the lower fluid with or without a horizontal bottom when two fluids are present are derived.
Abstract: The derivations are carried out for the velocity potentials of singularities moving with an arbitrary path either in the upper fluid or in the lower fluid with or without a horizontal bottom when two fluids are present. In such a case, the pressure distribution is no longer equal to a constant or zero at the free interface. Taking the influence of an upper fluid upon the lower fluid into consideration, a series of fundamental solutions in closed forms are presented in this paper.
TL;DR: In this article, the instability of nonlinear spherical membrane with large axisymmetric tensile deformations is investigated by using the bifurcation theory, and it is proved that all singular points of the nonlinear boundary value problem must be simple limit points.
Abstract: The problem on instability of nonlinear spherical membrane with large axisymmetric tensile deformations is investigated by using the bifurcation theory. It is proved that all singular points of the nonlinear boundary value problem must be simple limit points. The effect of loading and material parameters on the equilibrium state and its stability is discussed.
TL;DR: In this article, a nonlinear reaction-diffusion equation is studied numerically by a Petrov-Galerkin finite element method, which has been proved to be 2nd-order accurate in time and 4th-order in space.
Abstract: A nonlinear reaction-diffusion equation is studied numerically by a Petrov-Galerkin finite element method, which has been proved to be 2nd-order accurate in time and 4th-order in space. The comparison between the exact and numerical solutions of progressive waves shows that this numerical scheme is quite accurate, stable and efficient. It is also shown that any local disturbance will spread, have a full growth and finally form two progressive waves propagating in both directions. The shape and the speed of the long term progressive waves are determined by the system itself, and do not depend on the details of the initial values.
TL;DR: In this paper, a general method to find absolute expressions for different spins in a continuum, for which only principal axis expressions were available, is presented. But this method is not suitable for the case of the case where only the principal axis expression is available.
Abstract: The present paper offers a general method to find the absolute expressions for different spins in a continuum, for which only “the principal axis expressions” were available, and in this way it makes the further applications of these spins possible.