Showing papers in "Applied Mathematics and Mechanics-english Edition in 1987"
TL;DR: In this article, the field equation of micropolar fluid with general lubrication theory assumptions is simplified into two systems of coupled ordinary differential equation and analytical solutions of velocity and microrotation velocity are obtained.
Abstract: In this paper, the field equation of micropolar fluid with general lubrication theory assumptions is simplified into two systems of coupled ordinary differential equation. The analytical solutions of velocity and microrotation velocity are obtained. Micropolar fluid lubrication Reynolds equation is deduced. By means of numerical method, the characteristics of a finitely long journal bearing under various dynamic parameters, geometrical parameters and micropolar parameters are shown in curve form. These characteristics are pressure distribution, load capacity, coefficient of flow flux and coefficient of friction. Practical value of micropolar effects is shown, so micropolar fluid theory further closes to engineering application.
14 citations
TL;DR: In this paper, the image Sampsonlets with respect to the plane and by applying the constant density, the linear and the parabolic approximation, the analytic expressions in closed form for flow field are obtained.
Abstract: By distributing continuously the image Sampsonlets with respect to the plane and by applying the constant density, the linear and the parabolic approximation, the analytic expressions in closed form for flow field are obtained. The drag factor of the prolate spheroid and the Cassini oval are calculated for different slender ratios and different distances between the body and the plane. It is demonstrated that the proposed method is satisfactory both in convergence and accuracy. Comparison with existing results in the case of prolate spheroid shows that the coincidence is quite good.
13 citations
TL;DR: In this article, the authors derived the variational equation of circular corrugated plates by using Hamilton principle and adopted the perturbation variational method, in the first-order approximation.
Abstract: In this paper, first by using Hamilton principle, we derive the variational equation of circular corrugated plates. Taking the central maximum amplitude of circular corrugated plates as the perturbation parameter and adopting the perturbation variational method, in the first-order approximation, we obtain the natural frequency of linear vibration of circular corrugated plates and then the nonlinear natural frequency of the corrugated plates. By comparing with the linear results, the attempt of this paper is proved feasible.
13 citations
TL;DR: In this paper, the authors extend Poincare's nonlinear oscillation theory of discrete system to continuum mechanics and propose a method to calculate the periodic solution in the states of both resonance and nonresonance by means of the direct perturbation of partial differential equation and weighted integration.
Abstract: In this paper we extend Poincare's nonlinear oscillation theory of discrete system to continuum mechanics. First we investigate the existence conditions of periodic solution for linear continuum system in the states of resonance and nonresonance. By applying the results of linear theory, we prove that the main conclusion of Poincare's nonlinear oscillation theory can be extended to continuum mechanics. Besides, in this paper a new method is suggested to calculate the periodic solution in the states of both resonance and nonresonance by means of the direct perturbation of partial differential equation and weighted integration.
12 citations
TL;DR: In this article, the new forms of the differential equations of motion of the systems with higher-order nonholonomic constraints are obtained at first, and then the equivalence between these equations and the known equations is demonstrated.
Abstract: In this paper, the new forms of the differential equations of motion of the systems with higher-order nonholonomic constraints are obtained at first, and then the equivalence between these equations and the known equations is demonstrated. Finally an example is given to illustrate the application of our new equations.
9 citations
TL;DR: In this paper, the applicable ranges of one-equation and twoequation turbulence models with the viewpoint of similar theory are discussed, and the criterions of determining the applicable range of these models are given.
Abstract: Here, we are discussing the applicable ranges of one-equation and two-equation turbulence models with the viewpoint of similar theory. The criterions of determining the applicable ranges of these models are given.
9 citations
TL;DR: In this paper, the authors provided a rigorous solution of a free rectangular plate on the V.Z.Vlazov two-parameter elastic foundation by the method of superposition.
Abstract: This paper provides a rigorous solution of a free rectangular plate on the V.Z.Vlazov two-parameter elastic foundation by the method of superposition[1]. In this paper we derive basic solutions under the various boundary conditions. To superpose these basic solutions the most generally rigorous solution of a free rectangular plate on the two-parameter elastic foundation can be obtained. The solution strictly satisfies the differential equation of a plate on the two-parameter elastic model foundation, the boundary conditions of the free edges and the free corner conditions. Some numerical examples are presented. The calculated results show that when the plane dimension of plate is given and the ratio between the layer depth and the plate thick is equal to 15, the two-parameter elastic model is near the Winkler's. It shows that the Winkler model can be applied to the thinner layer.
8 citations
TL;DR: In this article, the authors extended the Schwarz principle to the case of dissimilar materials with co-circular cracks under concentrated force and moment and provided a series of particular results, in which two of them coincide with those in Ref.
Abstract: The method is very efficient by applying extended Schwarz principle integrated with the analysis of the singularity of complex stress functions to solve some plane-elastic problems under concentrated loads, in Ref[1], this method is used to deal with the elastic problems of homogeneous plane In this paper, it is extended to the case of dissimilar materials with co-circular cracks under concentrated force and moment For several typical cases the solutions of complex stress function in closed form are built up and the stress intensity factors are given From these solutions, we provide a series of particular results, in which two of them coincide with those in Refs [1] and [6]
7 citations
TL;DR: In this article, the unsteady natural convection flow in a square cavity at high Rayleigh number Ra=107 and 2×107 has been computed using cubic spline integration.
Abstract: The unsteady natural convection flow in a square cavity at high Rayleigh number Ra=107and 2×107has been computed using cubic spline integration. The required solutions to the two dimensional Navier-Stokes and energy equations have been obtained using two alternate numerical formulations on non-uniform grids. The main features of the transient flow have been briefly discussed. The results obtained by using the present method are in good agreement with the theoretical predictions[1,2].The steady state results have been compared with accurate solutions presented recently for Ra=107.
6 citations
TL;DR: In this article, the jumping problem of a circular thin plate with initial deflection was studied by using the method of two variables and the normal perturbation, and the authors obtained Nth-order uniformly valid asymptotic expansion of the solution of this problem.
Abstract: In this paper, the jumping problems of a circular thin plate with initial deflection are studied by using ‘the method of two variables’[3],[4] proposed by Jiang Fu-ru and the method of the normal perturbation (in this paper (1.1), (1.2)). We obtain Nth-order uniformly valid asymptotic expansion of the solution of this problem ((1.66), (1.67)). When the initial deflection vanishes the solution of a circular thinplate with initial deflection is reduced to the solution of the problems of the nonlinear bending of a circular thin plate[6]. If the initial deflection is largish and the signs of the initial deflection with the intensity of the transverse load are opposite, when the intensity of the transverse load reaches a certain value, the circular thin plate with initial deflection should produce the jumping phenomenon[8].
6 citations
TL;DR: In this paper, a series of papers have been published concerning the variational principles and generalized variational principle in elasticity such as [1] (1979), [6] (1980), [2,3] (1983) and [4,5] (1984).
Abstract: Since 1979, a series of papers have been published concerning the variational principles and generalized variational principles in elasticity such as [1] (1979), [6] (1980), [2,3] (1983) and [4,5] (1984). All these papers deal with the elastic body with linear stress-strain relations. In 1985, a book was published on generalized variational principles dealing with some nonlinear elastic body, but never going into detailed discussion. This paper discusses particularly variational principles and generalized variational principles for elastic body with nonlinear stress-strain relations. In these discussions, we find many interesting problems worth while to pay some attention. At the same time, these discussions are also instructive for linear elastic problems. When the strain is small, the high order terms may be neglected, the results of this paper may be simplified to the well-known principles in ordinary elasticity problems.
TL;DR: In this article, the authors generalize the Steiner problem on planes to general regular surfaces and show that the main result is the same as in this paper, but with a different formulation.
Abstract: In this paper we generalize the Steiner problem on planes to general regular surfaces. The main result is
TL;DR: In this article, the authors considered a second order ODE with a small positive parameter e in its highest derivative for periodic boundary values problem and proved that the solution of difference scheme in paper [1] uniformly converges to the original problem with order one.
Abstract: In this paper, we consider a second order ordinary differential equation with a small, positive parameter e in its highest derivative for periodic boundary values problem and prove that the solution of difference scheme in paper [1] uniformly converges to the solution of its original problem with order one.
TL;DR: In this article, the velocity fluctuations are separated into large and small vortexes, and the large vortexes consist of two parts, one comes from up-stream and around, the other is locally generated.
Abstract: Recently the k-e model has been widely used, but it is a kind of gradient model. Because the life-time of turbulence vortexes is very long, in common flow problems the influence of up-stream vortexes must be important, and the vortexes are not in quasi-equilibrium. So the usefulness of the k-e model and other gradient models is limited. In this paper, according to actual cases of the turbulence, the velocity fluctuations are separated into large and small vortexes, and the large vortexes consist of two parts, one comes from up-stream and around, the other is locally generated. Thus we get a turbulence model, which consists of three parts.
TL;DR: In this paper, the expressions for a kind of new rotlets in Stokes flow are derived by means of superposition of these rotlets, and the drag moment for rotating double spheres and multiple spheres along the smae axis is presented.
Abstract: In this paper the expressions for a kind of new rotlets in Stokes flow are derived. By means of superposition of this new rotlets, the drag moment for rotating double spheres and multiple spheres along the smae axis are presented. It has been demonstrated that drag moment for each sphere is the linear function of its angular velocity.
TL;DR: In this article, the authors studied the solution of differential equation with Dirac function and Heaviside function arising from discontinuous and impulsive excitation, and derived the equation of x(t) and x (t) by terms of property of distribution.
Abstract: In this paper, we study the solution of differential equation with Dirac function and Heaviside function, arising from discontinuous and impulsive excitation. Firstly, according to the theory of differential equation, we suggest, then we derive the equation of x
1
(t) and x
2
(t) by terms of property of distribution, and by solving x
1
(t) and x
2
(t) we obtain x(t); finally, we make a thorough investigation about periodic impulsive parametric excitation.
TL;DR: In this article, the existence of panchaos, panattractor and strange panattractor subsets was investigated under the framework of pan-systems methodology, and a certain obtained result indicated that Panchaos and Panattractor correspond respectively to fixed subsets of certain pansystems operators.
Abstract: The investigations about chaos, attractor and strange attractor are main subjects in nonlinear analysis. Under the framework of pansystems methodology, reference [1] discussed these problems and introduced the concepts of panchaos, panattractor and strange panattractor. These concepts omitted the condition of continuity, compactness, etc. and put stress on the properties of binary relations on a set. A certain obtained result indicates that panchaos, panattractor and strange panattractor correspond respectively to fixed subsets of certain pansystems operators. This paper continues the investigation of [1,2], discusses the existence of these pansystems fixed subsets, their construction and interrelations.
TL;DR: In this paper, an additional stiffness matrix of meridional geometric imperfections was formed by considering the imperfections as initial displacements based on reference, and the natural frequencies and models of rotational shell with symmetric geometric imperfection were analyzed by perturbation method.
Abstract: In this paper, an additional stiffness matrix of meridional geometric imperfections was formed by considering the geometric imperfections as initial displacements based on reference [7]. Then, natural frequencies and models of rotational shell with symmetric geometric imperfections were analysed by perturbation method. From the computed example, it was known that the effect of geometric imperfections of frequencies is to increase them, and the larger the range of imperfection, the more the frequencies would be increased.
TL;DR: In this paper, the von Karman's equations were reduced to equivalent integral equations which are nonlinear, coupled and singular, and the sequences of continuous function with general form were constructed using iterative technique.
Abstract: It is extremely difficult to obtain an exact solution of von Karman's equations because the equations are nonlinear and coupled. So far many approximate methods have been used to solve the large deflection problems except that only a few exact solutions have been ised to solve the large deflection problems except that only a few exact solutions have been investigated but no strict proof on convergence is presented yet. In this paper, first of all, we reduce the von Karman's equations to equivalent integral equations which are nonlinear, coupled and singular. Secondly the sequences of continuous function with general form are constructed using iterative technique. Based on the sequences to be uniformly convergent, we obtain analytical formula of exact solutions to von Karman's equations related to large deflection problems of circular plate and shallow spherical shell with clamped boundary subjected to a concentrated load at the centre.
TL;DR: The functional transformations of variational principles in elasticity are classified as three patterns: I relaxation pattern, II augmented pattern and III equivalent pattern as mentioned in this paper, and they can be classified as follows:
Abstract: The functional transformations of variational principles in elasticity are classified as three patterns: I relaxation pattern, II augmented pattern and III equivalent pattern.
TL;DR: In this paper, the equations of impact for a nonholonomic system described with generalized coordinated have been discussed in detail in the general references of classical dynamics, but these equations contain undetermined multipliers which made the problem complicated.
Abstract: The equations of impact for a nonholonomic system described with generalized coordinated have been discussed in detail in the general references of classical dynamics. But these equations contain undetermined multipliers which made the problem complicated.
TL;DR: In this article, the authors derived the general analytical expressions of the anisotropic plastic stress field near a singular point in both the cases of anti-plane and in-plane strains.
Abstract: On condition that any perfectly plastic stress component near a singular point is nothing but the function of θ only, making use of equilibrium equations and Hill anisotropic yield condition, we derive the general analytical expressions of the anisotropic plastic stress field near a singular point in both the cases of anti-plane and in-plane strains. Applying these general analytical expressions to the concrete cracks and the plane-strain bodies with a singular point, the anisotropic plastic stress fields at the tips of Mode I, Mode II, Mode III and mixed mode I–II cracks, and the limit loads of anisotropic plastic plane-strain bodies with a singular point are obtained.
TL;DR: In this article, the problem of stress analysis of plates with a circular hole reinforced by flange reinforcing member is addressed, where the reinforcement member is built up by setting shapes or bars with any section shape on both sides of the plates along the edge of the hole.
Abstract: This paper deals with the problem of stress analysis of plates with a circular hole reinforced by flange reinforcing member. The so called flange reinforcing member here means that the reinforcing member is built up by setting shapes or bars with any section shape on both sides of the plates along the edge of the hole. Two cases of external loads are considered. In one case the external loads are stresses σX(∞), σY(∞) and τXY(∞),acting at infinite point of the plate, and in the other the external loads are linear distributed normal stresses. The procedure of solving the problems mentioned above consists of three steps. Firstly, the reinforcing member is taken out from the plates and considered to be a circular bar being solved to determine its deformation under the action of radial force q0(θ) and tangential force t0(θ)which are forces acting upon each other between reinforcing member and plate. Secondly, the displacements of plate with a circular hole under the action of q0(θ) and t0(θ)and external loads are determined. Finally, forces q0(θ) and t0(θ)are obtained by the compatibility of deformations between reinforcing member and plate. Then the internal forces and displacements of reinforcing member and plate are deduced from q0(θ) and t0(θ)obtained.
TL;DR: In this article, an axisymmetric nonlinear mode has been derived for the instability problem of flow through a circular cross section, where the coefficient of it can be negative with Reynolds number increasing due to the complex interaction between molecular diffusion and convection.
Abstract: An investigation is described for instability problem of flow through a.pipe of circular cross section. As a disturbance motion, we consider an axisymmetric nonlinear mode. An associated amplitude or modulation equation has been derived for this perturbation. This equation belongs to the diffusion type. The coefficient of it can be negative with Reynolds number increasing, because of the complex interaction between molecular diffusion and convection. The negative diffusion, when it occurs, cause a concentration and focusing of energy within the decaying slug, acting as a role of reversing natural decays.
TL;DR: In this article, the application of Dynamic-Relaxation (DR) method to the problems of nonlinear bending of rectangular plates laminated of bimodular composite materials is investigated.
Abstract: This paper investigates the application of Dynamic-Relaxation (DR) method to the problems of nonlinear bending of rectangular plates laminated of bimodular composite materials. The classical lamination theory and a shear deformation theory of layered composite plates, taking account of large rotations (in the von Karman sense) are employed separately to analyze the subject.
TL;DR: In this paper, the extension strains and the shearing strains are linearly expressed in terms of nine partial derivatives of the displacement function (ui,uj,uh)=u(xi,xj,xk) and it is impossible for the inverse proposition to sep up a system of the above six equations in expressing the nine components of matrix.
Abstract: This paper is neither laudatory nor derogatory but it simply contrasts with what might be called elastostatic (or static topology), a proposition of the famous six equations. The extension strains and the shearing strains
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which were derived by A.L. Cauchy, are linearly expressed in terms of nine partial derivatives of the displacement function (ui,uj,uh)=u(xi,xj,xk) and it is impossible for the inverse proposition to sep up a system of the above six equations in expressing the nine components of matrix (∂(ui,uj,uh)/∂(xi,xj,xk)). This is due to the fact that our geometrical representations of deformation at a given point are as yet incomplete[1]. On the other hand, in more geometrical language this theorem is not true to any triangle, except orthogonal, for “squared length” in space[2].
TL;DR: In this article, the general solution of small deflection problem or the exact solution of large deflection problems for the corrugated or ribreinforced plates and shells as special cases is included in this paper.
Abstract: This work is the continuation of the discussion of Refs. [1–5]. In this paper: . The general solution of small deflection problem or the exact solution of large deflection problem for the corrugated or ribreinforced plates and shells as special cases is included in this paper.
TL;DR: In this paper, the distributions of displacements of circular footing plates on soils and reactions of soils under arbitrary loads using semi-analytical finite element method were calculated and compared with those by F E M. Vlazov's solution in the case of axisymmetry.
Abstract: Modelling soils by two-parameter foundation model, this paper calculates the distributions of displacements of circular footing plates on soils and reactions of soils under arbitrary loads using semi-analytical finite element method. And it improves V.Z. Vlazov's solution in the case of axisymmetry. The results agree well in comparison with those by F E M. At the same time, the boundary conditions of circular plates on soils are discussed.
TL;DR: In this article, the singular perturbation problem of the parabolic partial differential equation is discussed and the mesh size in the neighbourhood of the boundary layer is reduced so that the typical feature of boundary layer will not be lost.
Abstract: In this paper, we discuss the singular perturbation problem of the parabolic partial differential equation. As usual, we must reduce the mesh size in the neighbourhood of the boundary layer so that typical feature of the boundary layer will not be lost. Then we need very large operational quantity when mesh sizes are getting too small.
TL;DR: In this article, a complex variable function method for hole shape optimization problem in an elastic plane is presented, where the coefficients in conformal mapping function are revised by iteration step by step until the largest circumferential stress in absolute value is reduced to the second largest stress.
Abstract: In this paper, a complex variable function method for solving the hole shape optimization problem in an elastic plane is presented. In this method, the stresses in hole problems are analysed by taking advantage of the efficiency of the complex variable function method. To optimize the hole shape, the coeffecients in conformal mapping functions are taken as design variables, and the sensitivity analysis and gradient methods are used to reduce the largest circumferential stress in absolute value and at the same time to make the second largest circumferential stress in absolute value not to exceed the largest one (in fact, these two stresses are the stationary values of the circumferential stresses). The coefficients in conformal mapping function are revised by iteration step by step until the largest circumferential stress in absolute value is reduced to the second largest stress. This method guarantees the continuity, differentiability and accuracy of the stress solution along the boundary, and it is evident that this method is better than either the difference method or the finite element method.