Showing papers in "Applied Mathematics and Mechanics-english Edition in 1994"
TL;DR: In this article, a general solution of displacement and electric potential function denoted by unique potential function which satisfies specific partiality equations is provided to analyze the mechanical-electrical coupling behavior of piezoelectric material which contains defects such as cavity, inclusion, penny shape crack, and so on.
Abstract: According to the structure feature of the governing equations of space axisymmetric problem in transversely isotropic piezoelectric material, using the method of introducing potential function one by one, in this paper we obtain the so-called general solution of displacement and electric potential function denoted by unique potential function which satisfies specific partiality equations. As an applying example of the general solution, we solve problem of semi-infinite body made of piezoelectric material, on the surface of the semi-infinite body a concentrative force is applied, and get the analytic formulations of stress and electric displacement components. The general solution provided by this paper can be used as a tool to analyse the mechanical-electrical coupling behavior of piezoelectric material which contains defects such as cavity, inclusion, penny-shape crack, and so on. The result of the solved problem can be used directly to analyse contact problems which take place between two piezoelectric bodies or piezoelectric body and elastic body.
32 citations
TL;DR: In this paper, the governing equations of plane elasticity in sectorial domain were derived to be in Hamiltoinan form via variable substitutes and variational principles, and the method of separation of variables and eigenfunction expansion method were derive1 to solve the finite element analytically for the sectorialdomain elasticity problem, so that such kind of analytical element can be installed into FEM program systems.
Abstract: The governing equations of plane elasticity in sectorial domain are derived to be in Hamiltoinan form via variable substitutes and variational principles. The method of separation of variables and eigenfunction expansion method are derive1 to solve the finite element analytically for the sectorial domain elasticity problem, so that such kind of analytical element can be installed into FEM program systems. It demonstrates the potential of the Hamiltonian system theory and symplectic mathematics.
30 citations
TL;DR: By means of CUSP model of catastrophe theory, Wang et al. as discussed by the authors studied the physics process of rockburst occurred on circular chamber and got the critical depth of plastic softening area of chamber that is valuable in the controlling engineering of rock burst.
Abstract: By means of CUSP model of catastrophe theory, this paper has studied the physics process of rockburst occurred on circular chamber. The present paper has not only described the instability process of rockburst more deeply, but also got the critical depth of plastic softening area of chamber that is valuable in the controlling engineering of rockburst. The chamber displacement jump and energy liberation have been derived. The influence of rock parameters on the rockburst has been discussed.
15 citations
TL;DR: In this paper, an analysis of the constitutive relations between the internal forces and deformations of discrete rectangular reticulated structures is given based on fundamental assumptions, and an equivalent continuum model is adopted and the application of the principle of virtual work leads to non-linear governing equations and corresponding boundary conditions.
Abstract: Based on fundamental assumptions, an analysis of the constitutive relations between the internal forces and deformations of discrete rectangular reticulated structures is given. On the basis of this, an equivalent continuum model is adopted and the application of the principle of virtual work leads to non-linear governing equations and corresponding boundary conditions.
11 citations
TL;DR: In this paper, the Ishikawa iteration process converges strongly to a solution of the equation TX=f wheh T is Lipschitzian and local strongly accretive in X.
Abstract: Suppose that K is a non-empty subset of a uniformly smooth Banach space X. Let T:K→X be a Lipschitz local strictly pseudocontractive mapping. In this paper, the iterative sequence which converges strongly to the unique fixed point of T is given. A related result deals with the problem that the Ishikawa iteration process converges strongly to a solution of the equation TX=f wheh T is Lipschitzian and local strongly accretive in X.
10 citations
TL;DR: In this article, the authors study the dynamic behavior of dissipative soliton equation: existence of attractor, geometrical structure of attractors, dynamic behavior under the parametric perturbation, and estimate of fractal dimension of the attractor.
Abstract: In the paper, we study longtime dynamic behavior of dissipative soliton equation: existence of attractor, geometrical structure of attractor, dynamic behavior under the parametric perturbation of dissipative soliton equation, estimate of fractal dimension of attractor.
8 citations
TL;DR: In this paper, the authors gave the approximate equations of the eccentric cylindrical thin shell under small deflections, and by means of the analytical method, they solved the equations.
Abstract: The present paper gives the approximate equations of the eccentric cylindrical thin shell under small deflections. By means of the analytical method, we solved the equations. Thus the relations between the stress, the displacement and the eccentricity of the eccentric cylindrical thin shell are obtained.
8 citations
TL;DR: In this paper, the postbuckling behavior of Reissner's moderately thick plates and sandwich plates is investigated and the fundamental equations and boundary conditions are expressed in unified dimensionless form.
Abstract: Postbuckling behavior is investigated for Rectangular Reissner's moderately thick plates and sandwich plates. The fundamental equations and boundary conditions are expressed in unified dimensionless form for rectangular moderately thick plates and sandwich plates. Exact solutions of series form with a number of different boundary conditions, especially with unsymmetrical boundary conditions, are obtained by developing a new technique of mixed Fourier series in nonlinear analysis. The nonlinear partial differential equations are reduced to an infinite set of simultaneous nonlinear algebraic equations, which are truncated by iteration in numerical computations.
8 citations
TL;DR: In this article, a non-linear vibration analysis of rectangular reticulated shallow shells was studied by applying nonlinear elastic theory of such structures established by the author, and the amplitude-frequency relations for free vibration and forced vibration due to harmonic force were derived with the aid of the regular perturbation emthod and Galerkin procedure, respectively.
Abstract: This paper deals with non-linear vibration of rectangular reticulated shallow shells by applying non-linear elastic theory of such structures established by the author. Using the assumed (generalized) Fourier series solutions for transverse deflection (lattice joint transverse displacement) and force function, weighted means of the trial functions lead to the relations among the coefficients related to the solutions and vibration equation which determines the unknown time function, and then the amplitude-frequency relations for free vibration and forced vibration due to harmonic force are derived with the aid of the regular perturbation emthod and Galerkin procedure, respectively. Numerical examples are given as well.
7 citations
TL;DR: In this article, a numerical method for three-dimensional problem and the analysis of its stability are established and a numerical result for a practical model is given, which shows that the abnormal pressure and paleo-temperature computed are reasonable and display physical characteristics clearly as well.
Abstract: Numerical simulation for evolutionary history of an oil- and gas-bearing basin is to repeat geological and thermodynamic history of basin evolution on a computer and then to quantitate petroleum generation, accumulation and migration. The mathematical model describing geological and thermodynamic history of the basin evolution is characterised by an initial-boundary value problem of a system of nonlinear partial differential equations. In the present paper, a numerical method for three-dimensional problem and the analysis of its stability are established and a numerical result for a practical model is given, which shows that the abnormal pressure and paleo-temperature computed are reasonable and display physical characteristics clearly as well.
7 citations
TL;DR: In this paper, an energy principle, zero different principle of coupled systems in photoelasticity, from which the potential energy, the complementary energy, generalized potential energy and generalized complementary energy variational principles are derived.
Abstract: This paper presents an energy principle, zero different principle of coupled systems in photoelasticity, from which the potential energy, the complementary energy, generalized potential energy and generalized complementary energy variational principles of the coupled systems in photoelasticity are derived.
TL;DR: In this article, necessary and sufficient conditions for absolute stability of several classes of direct control systems are given, and two simplified forms of the control systems obtained twice[2.4] are discussed.
Abstract: In this paper, some necessary and sufficient conditions for absolute stability of several classes of direct control system are given, and the two simplified forms of the control systems obtained twice[2.4] are discussed. The corresponding results in [7–12] are improved.
TL;DR: In this article, the fundamental equations of the axisymmetric large amplitude free vibration for circular sandwich plates are derived by means of Hamilton principle, and then the preceding fundamental equations are simplified considerably.
Abstract: In this paper, fundamental equations of the axisymmetric large amplitude free vibration for circular sandwich plates are derived by means of Hamilton principle. In most cases, the sandwich plates are composed of very thin faces, then the preceding fundamental equations are simplified considerably. For an illustrative example, a circular sandwich plate with edge clamped but free to slip is considered, and then we got a pure analytic solution of the axisymmetric large amplitude free vibration with the aid of the modified iteration method, and derived an analytic relation for the amplitude-frequency response.
TL;DR: In this article, the authors draw some common fixed point theorems for nonlinear hybrid contraction mappings on probabilistic metric spaces with a convex structure, and show that the convergence of these mappings can be characterized by the following properties:
Abstract: In this paper we draw some coincidence and common fixed point theorems for nonlinear hybrid contraction mappings on probabilistic metric spaces with a convex structure.
TL;DR: In this paper, the flow law of the laminar helical flow of the power law fluid and Bingham fluid in eccentric annular space and the determination of the flow state were studied.
Abstract: Many problems in petroleum and chemical industry can be reduced to the solutions of the helical flow of Non-newtonian fluid in eccentric annular space. This paper studies the flow law of the laminar helical flow of the power law fluid and Bingham fluid in eccentric annular space and the determination of the flow state. In theory, by the principle of the fluid mechanics, with methematical methods, based on our theory of the helical flow in concentric annular space and through the infinite subdivision method for the flow field of eccentric annular space helical flow, the apparent viscosity distribution, the velocity distribution, the flow rate and the pressure drop equation of the field can be given, and then the stability parameter, characterizing the transition from laminar to turbulent flow, is established.
TL;DR: The photogravitational restricted three-body problem in which the mass reduction factors of two primaries q1, q2 e −∞,1] are studied and an analytic method to estimate the number of libration points and to calculate their location is given in this article.
Abstract: The photogravitational restricted three-body problem in which the mass reduction factors of two primaries q1, q2 e −∞,1] are studied and an analytic method to estimate the number of libration points and to calculate their location is given in this paper. The results show that in photogravitational restricted three-body problem, the number of libration points is from one to seven for different q1 and q2. As application, the motion of dust grain like comet tail in the solar system is also discussed.
TL;DR: In this article, the eigenvalue problem of the structures with interval parameters is transferred into two different eigen value problems to be solved, and the perturbation method is applied to the vibration problem.
Abstract: When the parameters of the structures are uncertain, the structural natural frequencies become uncertain. In this paper, we deal with the vibration problem of the structure with interval parameters, the eigenvalue problem of the structures with interval parameters is transferrd into two different eigenvalue problems to be solved. The perturbation method is applied to the vibration problem of the structures with interval parameters, the numerical results show that the proposed method is sufficiently accurate and needs little computational efforts.
TL;DR: In this paper, the problems of nonlinear unsymmetrical bending for cylindrically orthotropic circular plate are studied by using the method of two-variable, and the uniformly valid asymptotic solutions of Nth-order for e1 and Mth order for e2 are obtained.
Abstract: In this paper, the problems of nonlinear unsymmetrical bending for cylindrically orthotropic circular plate are studied by using “the method of two-variable”[1], and the uniformly valid asymptotic solutions of Nth-order for e1 and Mth-order for e2 are obtained
TL;DR: In this article, the singularity of stress and strain at the tip of a three-dimensional notch is analyzed by the power expansion method, the eigenequation of the notch is gained through the boundary conditions and the eigenvalues under different inner angles of a notch are obtained.
Abstract: The singularity of stress and strain at the tip of three-dimensional notch is analysed by the power expansion method, the eigenequation of the notch is gained through the boundary conditions of the notch, the eigenvalues under different inner angles of the notch are obtained, the expression of stress and strain at the tip of the notch is finally derived.
TL;DR: In this article, a Fourier pseudospectral-finite difference scheme is proposed for three-dimensional vorticity equation with unilaterally periodic boundary condition, and generalized stability and convergence are analyzed.
Abstract: A Fourier pseudospectral-finite difference scheme is proposed for three-dimensional vorticity equation with unilaterally periodic boundary condition. The generalized stability and convergence are analyzed. The numerical results show the advantage of this method.
TL;DR: In this paper, the inverse problem in calculus of variations is studied and a new concept called variational integral is introduced, which is used to systematically study the inverse problems in the calculus.
Abstract: The inverse problem in calculus of variations is studied. By introducing a new concept called Variational Integral, a new method to systematically study the inverse problem in calculus of variations is given. Using this new method to the elastodynamics and hydrodynamics of viscous fluids, some kinds of variational principles and generalized variational principles are obtained respectively.
TL;DR: In this article, three kinds of forms for Noether's conservation laws of holonomic non-conservative dynamical systems in generalized mechanics are given, and three different forms for non-consistency laws of non-convex systems are given.
Abstract: In the present paper, three kinds of forms for Noether's conservation laws of holonomic nonconservative dynamical systems in generalized mechanics are given.
TL;DR: In this paper, the authors prove the existence of solutions to the generalized strongly nonlinear quasi-complementarity problems and the convergence of the iterative sequences generated by the algorithm.
Abstract: Using the algorithm in this paper, we prove the existence of solutions to the generalized strongly nonlinear quasi-complementarity problems and the convergence of the iterative sequences generated by the algorithm. Our results improve and extend the corresponding results of Noor and Chang-Huang. Moreover, a more general iterative algorithm for finding the approximate solution of generalized strongly nonlinear quasicomplementarity problems is also given. It is shown that the approximate solution obtained by the iterative scheme converges to the exact solution of this quasi-complementarity problem.
TL;DR: In this article, the free bending vibration of an annular cylindrical tank partially filled with liquid in the consideration of surface wave was studied. And the exact formulae of the mode shape functions and frequencies were deduced by means of computer.
Abstract: This paper studies the problem of free bending vibration of annular cylindrical tank partially filled with liquid in the consideration of surface wave. The exact formulae of the mode shape functions and frequencies are deduced. Results can be obtained by means of computer. The analysis shows that the effect of liquid on vibration of annular cylindrical tank is equivalent to different generalized distributive masses attached to inner and outer cylinders respectively.
TL;DR: In this paper, the equations describing the flow of a viscoplastic fluid on a rotating disk are derived and are solved by perturbation technique and numerical computation respectively for 2 cases, which makes it possible to calculate the thickness distribution of film.
Abstract: The equations describing the flow of a viscoplastic fluid on a rotating disk are derived and are solved by perturbation technique and numerical computation respectively for 2 cases. This makes it possible to calculate the thickness distribution of film. Two kinds of distribution of thickness have been found. For the viscoplastic fluid for which both viscosity and yield stress are independent of radial coordinate r, the thickness h decreases with increasing r. For a Bingham fluid for which both viscosity and yield stress are function of time and r, the thickness h increases with increasing r.
TL;DR: In this article, transfer open or closed valued mapping is introduced to generalize the KKM theorem on H-space, which generalizes slightly the corresponding results in [1, 2, 4, 5, 6, 7].
Abstract: In this paper, we introduce a class of generalized mapping called transfer open or closed valued mapping to generalize the KKM theorem on H-space. Then as applications, using our H-KKM theorem, we prove some coincidence theorems, matching theorems and vector valued minimax inequalities which generalize slightly the corresponding results in [1, 2, 4, 5, 6, 7].
TL;DR: In this article, the composite laminates subjected to pure bending are modelled by using 3-D anisotropic finite elements and the distributions of stress and strain along the thickness are presented.
Abstract: In this paper, the composite, laminates subjected to pure bending are modelled by using 3-D anisotropic finite elements and the distributions of stress and strain along the thickness are presented. The numerical results show that there is a stress concentration near the bonding interface in the central region (far from traction boundaries and free edges) of symmetric angle-ply laminates, which should be called “interlaminar effect”. The abrupt change of the mechanical behavior of material on the interfaces causes interlaminar stresses. The laminates are in 3-D stress state near the interfaces. The strain distribution of the 3-D numerical model is different from the strain hypothesis of the classical laminate theory based on the Kirchhoff-Love hypotheses of straight inextensional normals.
TL;DR: In this paper, four sufficiency theorems of existence of periodic solutions for a class of retarded functional differential equations are given, and an example of application is given at the end.
Abstract: In this paper, four sufficiency theorems of existence of periodic solutions for a class of retarded functional differential equations are given. The result of these theorems is better than the well-known Yoshizawa’s periodic solution theorem. An example of application is given at the end.
TL;DR: In this paper, a set of equations depicting the nonlinear interactions of barotropic Rossby waves are derived, the topography and Ekman friction are involved in the equations, and the intrinsic frequencies of the secondary waves can be varied.
Abstract: In the frame of weak nonlinear theory, a set of equations depicting the nonlinear interactions of barotropic Rossby waves are derived, the topography and Ekman friction are involved in the equations. Starting from the equations, we investigate the interaction of three Rossby wave packets with narrow-spread in wave vectors. When an intense primary pump Rossby wave with amplitude larger than a threshold propagates through the atmosphere, the amplitude of one Rossby wave packet with scale greater than the primary one and one Rossby wave packet with scale smaller than the primary one grow exponentially through three wave interactions, the intrinsic frequencies of the secondary waves can be varied. The threshold and the variation of the intrinsic frequencies of the secondary waves are related to the Ekman friction frequency dismatch, topography and spatial evolution of the secondary Rossby wave packets.
TL;DR: In this paper, a new equilibrium existence theorem for generalized games with uncountable number of agents, noncompact choice sets and general preference correspondences which do neither have open graph nor have open lower sections was proved.
Abstract: In the present paper, we prove a new equilibrium existence theorem for generalized games with uncountable number of agents, noncompact choice sets and general preference correspondences which do neither have open graph nor have open lower sections. This theorem improves a recent result of Kim.