Showing papers in "Applied Mathematics and Mechanics-english Edition in 1984"
TL;DR: In this paper, the variational principles of hydrodynamic problems for the incompressible and compressible viscous fluids are established, which are principles of maximum power losses, and they are also discussed on the basis of Lagrangian multiplier methods.
Abstract: In this paper, the variational principles of hydrodynamic problems for the incompressible and compressible viscous fluids are established. These principles are principles of maximum power losses. Their generalized variational principles are also discussed on the basis of Lagrangian multiplier methods.
16 citations
TL;DR: On the basis of the anology with quantum electrodynamics, Dirac equation of elastic wave-phonon is developed and the fission of spectrum line of monochoromatic elastic wave under the action of an external field is studied in this article.
Abstract: On the basis of the anology with quantum electrodynamics, Dirac equation of elastic wave-phonon is developed and the fission of spectrum line of monochoromatic elastic wave under the action of an external field is studied in this paper.
11 citations
TL;DR: In this article, the Euler equation of the deflection of clastic thin plate is reduced to the equation with schrodinger form by the principle of quantum electro-dynamics.
Abstract: In this paper the Euler equation of the deflection of clastic thin plate is reduced to the equation with schrodinger form by the principle of quantum electro-dynamics. Then we can obtain the general solution of deflection of eleastic thin bending plate by the joint action of dynamical lateral pressure, force in central surface and external field on the elastic base.
10 citations
TL;DR: In this article, a sort of recognition theory and operations research of large scale systems are developed within the framework of pansystems methodology, which discuss some fundamental problems of interdisciplines from the viewpoint of generalized system-transformation-symmetry in things mechanism.
Abstract: In this work, a sort of recognition theory and operations research of large scale systems are developed within the framework of pansystems methodology. We establish a series of theorems concerning pansystems relations, which discuss some fundamental problems of interdisciplines from the viewpoint of generalized system-transformation-symmetry in things mechanism, and are connected closely with mathematical physics systems thinking science bioecological sciences and the methodological investigation of mechanical foundation. This paper offers 100 pansystems theorems.
10 citations
TL;DR: In this article, the authors classified variational principles in elasticity according to the differences in the constraints used in these principles, and showed that the stress-strain relations are the constraint conditions in all these variational principle, and cannot be removed by the method of linear Lagrange multiplier.
Abstract: In this paper, variational principels in elasticity are classified according to the differences in the constraints used in these principles. It is shown in a previous paper [4] that the stress-strain relations are the constraint conditions in all these variational principles, and cannot be removed by the method of linear Lagrange multiplier. The other possible constraints are four of them: (1) equations of equilibrium, (2) strain-displacement relations, (3) boundary conditions of given external forces and (4) boundary conditions of given boundary displacements. In variational principles of elasticity, some of them have only one kind of such constraints, some have two kinds or three kinds of constraints and at the most four kinds of constraints. Thus, we have altogether 15 kinds of possible variational principles. However, for every possible variational principle, either the strain energy density or the complementary energy density may be used. Hence, there are altogether 30 classes of functional of variational principles in elasticity. In this paper, all these functionals are tabulated in detail.
9 citations
TL;DR: The dynamic stability of a thin plate in supersonic flow based on 2-dimensional linear theory leads to the study of a new problem in mathematical physics: complex eigenvalue problem for a non-self-adjoint fourth-order integro-differential equation of Volterra's type as discussed by the authors.
Abstract: The dynamic stability of a thin plate in supersonic flow based on 2-dimensional linear theory leads to the study of a new problem in mathematical physics: complex eigenvalue problem for a non-self-adjoint fourth-order integro-differential equation of Volterra's type.
7 citations
TL;DR: In this paper, the modified Castigliano's theorem is presented, which is more convenient and more extensive for applications than the classical Castigliana's theorem, and can be used for many applications.
Abstract: This paper gives the modified Castigliano"s theorem, which is more convenient and more extensive for applications than the classical Castigliano"s theorem.
7 citations
TL;DR: In this article, a review of nonlinear bending problems of plates and shells is presented by means of the technique of undetermined small parameters, which can be used to solve the problem of plate bending.
Abstract: This paper presents a review which tackles some nonlinear bending problems of plates and shells in a unified way by means of the technique of undetermined small parameters.
7 citations
TL;DR: In this article, the authors studied the unsymmetrical bending of elastic flexible plates under various supports in case the tensile force acting on its boundary is zero, and showed that the bending of flexible flexible plates can be modeled as a tensile warping.
Abstract: In this paper we study the unsymmetrical bending of elastic flexible plates under various supports in case the tensile force acting on its boundary is zero.
7 citations
TL;DR: In this article, the authors discuss the existence, the structure and the number of fixed subsets in fixed pansystems, and discuss the relation between the existence and number of subsets.
Abstract: In this paper, we continue the research of fixed pansystems theorems presented in ref [1], and discuss the existence, the structure and the number of fixed subsets.
7 citations
TL;DR: In this paper, fixed point theorems for fuzzy mappings are presented, whose results generalize and improve the results of [3] and give a partial answer to the unsolved problem suggested in [1].
Abstract: Fixed point theorems for fuzzy mappings are of fundamental importance in fuzzy mathematical theory and application investigation. This paper pressents some new fixed point theorems for fuzzy mapping, whose results generalize and improve the results of [3] and give a partial answer to the unsolved problem suggested in [1].
TL;DR: In this article, a linear approximation of the line continuous distribution method of singularities is proposed to treat the creeping motion of the arbitrary pointed prolate axisymmetrical body, and analytic expressions in closed form for the flow field are obtained.
Abstract: The linear approximation of the line continuous distribution method of singularities is proposed to treat the creeping motion of the arbitrary prolate axisymmetrical body. The analytic expressions in closed form for the flow field are obtained. The numerical results for the proiate spheroid and Cassini oval demonstrate that the convergence and the accuracy of the proposen method are better that the constant density approximation. Furthermore, it can be applied to greater slender ratio. In this paper the example is yielded to show that the linear approximation of the singularities for the density on the partitioned segments can be utilized to consider the creeping motion of the arhitrary pointed prolate axisymmetrical body.
TL;DR: In this paper, the basic equations governing the motion of a stratified fluid, a kind of the generalized Boussinesq equations, were established on the basis of Bousminesq's shallow water theory, and then by way of them, the weak interaction of two pairs of obliquely colliding solitary waves, give the second-order approximate solutions for wave profiles and maximum amplitudes, as well as conclude that when the included angle between the directions of propagation of impinging solitary waves is less than 120°, the effect of the oblique interaction is stronger than that
Abstract: In this paper, on the basis of Boussinesq's shallow water theory, we establish the basic equations governing the motion of a stratified fluid, a kind of the generalized Boussinesq equations. And then by way of them, we study the weak interaction of two pairs of obliquely colliding solitary waves, give the second-order approximate solutions for wave profiles and maximum amplitudes, as well as conclude that when the included angle between the directions of propagation of impinging solitary waves is less than 120°, the effect of oblique interaction is stronger than that of the head-on one, but when the angle concerned is greater than 120°, the former is slightly weaker than the latter.
TL;DR: In this article, the perturbation method about two parameters is applied to the problem of large deflection of a cricular plate with exponentially varying thickness under uniform pressure, and an asymptotic solution up to the third-order is derived.
Abstract: In this paper the perturbation method about two parameters is applied to the problem of large deflection of a cricular plate with exponentially varying thickness under uniform pressure. An asymptotic solution up to the third-order is derived. In comparison with the exact solutions in special cases, the asymptotic solution shows a precise accuracy.
TL;DR: In this paper, the problem of bending a rectangular plate on the elastic foundation is solved by the method of superposition, which satisfies the differential equation, the boundary conditions of the edges and the free corners.
Abstract: In the theory of elastic thin plates, the bending of a rectangular plate on the elastic foundation is also a difficult problem. This paper provides a rigorous solution by the method of superposition. It satisfies the differential equation, the boundary conditions of the edges and the free corners. Thus we are led to a system of infinite simultaneous equations. The problem solved is for a plate with a concentrated load at its center. The reactive forces from the foundation should be made to be in equilibrium with the concentrated force to see whether our calculation is correct or not.
TL;DR: In this paper, the nonlinear bendings for the orthotropic rectangular thin plates under various supports are studied, and the authors show that the bendings of these thin plates are nonlinear.
Abstract: In this paper, the nonlinear bendings for the orthotropic rectangular thin plates under various supports are studied.
TL;DR: Based on the interaction of asperities and upper bound approach, a mathematical model for simulation of friction phenomenon between dies and workpiece is proposed in this paper, where it is found that in addition to adhering, tearing, ploughing etc., as perities workpiece can move wave-like along the surface layer and under certain circumstances they may disappear.
Abstract: Based on the interaction of asperities and upperbound approach a mathematical model for simulation of friction phenomenon between dies and workpiece is proposed. Optimizing the mathematical model with respect to several variables it is found that in addition to adhering, tearing, ploughing, etc., asperities workpiece can move wave-like along the surface layer and under certain circumstances they may disappear. If the asperities wavily move along the surface layer the friction coefficient depends on the geometry of asperities. However, the bonding strength of asperities has no significant influence on friction coefficient. The depth of the plastic deformation layer is related to the geometry of asperities, too. The soundness of the prerequisite of the proposed model and some analytical results were verified by experiments.
TL;DR: Several new random fixed point theorems for random set-valued mappings and for a system ofRandom fixed pointTheorems improved and generalize many recent findings in [4–7, 9, 11–17].
Abstract: In this paper, first we show several new random fixed point theorems for random set-valued mappings and for a system of random set-valued mappings. Then, some applications of our results are given for the existence and uniqueness of random solution for a system of nonlinear random integral and differential equations. Our theorems improved and generalize many recent findings in [4–7, 9, 11–17].
Journal Article•
TL;DR: In this article, a method of interpolating a velocity field from the data measured at a few points in a region and at all points on its boundary is proposed, which has zero divergence and differs from the linear interpolation in the sense of the least-squares error.
Abstract: A method of interpolating a velocity field from the data measured at a few points in a region and at all points on its boundary is proposed. The interpolated field has zero divergence and differs from the linear interpolation in the sense of the least-squares error.
TL;DR: In this paper, the generalized Whittaker equation was extended to non-holonomic systems and the generalized generalized Whaddaker equations were obtained. And then these equations were transformed into Nielsen's form.
Abstract: In 1904, using the energy integral Whittaker studied the reduction of a dynamical problem to a problem with fewer degrees of freedom for the holonomic conservative systems and obtained the Whittaker equation[1]. In this article, Whittaker equations are extended to non-holonomic systems and the generalized Whittaker equations are obtained. And then these equations are transformed into Nielsen's form. Finally an example is given.
TL;DR: In this article, the structural character of fixed subsets, the criterion of existence of the least fixed subset, and the numbering formula of the fixed subset and minimal fixed subset are discussed.
Abstract: Pansymmetry is the abstract of symmetry, stability and other concepts in physics and so on. Fixed pansystems theorems portray a typical pansymmetry of systemic structure. The present paper complements and extends the work in [1]–[3] concerned in fixed pansystems theorems. It gives in finite case the structural character of fixed subsets; the criterion of existence of the least fixed subset, and the numbering formula of fixed subsets and minimal fixed subsets.
TL;DR: In this paper, a new potential ψ which is defined as the correlative potential is developed, which is different from the classical scalar potential ϕ and the vector potential developed by Helmholtz.
Abstract: This paper is a continuation of Paper [1].
1.
A new potential ψ which is defined as the correlative potential is developed in this paper. The potential ψ is different from the classical scalar potential ϕ and the vector potential\(A\) developed by Helmholtz. The new formulae of the solution of eqs.\(
abla \times \mathop f\limits^ \to = \mathop \infty \limits^ \to .
abla \cdot \mathop f\limits^ \to = p\) are given in terms of ψ.
2.
In the time-varying electromagnetic field, two new retarded potentials, the electric type retarded correlative potential ψe and the magnetic type retarded correlative potential ψe, which are distinct from the classical retarded potentials\(A\) and ϕ, are used to solve Maxwell equations. The new formulae of solution of Maxwell equation are given in terms of ψe and ψm.
3.
The methods for constructing a rotational field with given curl function (vorticity) is proposed.
TL;DR: In this paper, the authors extended these results to vector boundary value problems, under analogous stability conditions on the solutionu=u(t) of the reduced equationO=h(t,u).
Abstract: Some authors employed the method and technique of differential inequalities to obtain fairly general results concerning the existence and asymptotic behavior, as ɛ→∩+, of the solutions of scalar boundary value problems
$$\varepsilon u'' = h(t, y), a< t< b, y(a, \varepsilon ) = A, y(b, \varepsilon ) = B$$
, In this paper, we extend these results to vector boundary value problems, under analogous stability conditions on the solutionu=u(t) of the reduced equationO=h(t,u). Two types of asymptotic behavior are studied, depending on whether the reduced solutionu(t) has or does not have a continuous first derivative in (a, b) leading to the phenomena of boundary and angular layers.
TL;DR: In this paper, analytical expressions of the pressure distribution, velocity distribution and the rate of flow between conical surfaces are found by using the method of iterative approximate solution when the inertia terms of the Navier-Stokes equations in conical coordinates are taken into account.
Abstract: In this paper, analytical calculation expressions of the pressure distribution, velocity distribution and the rate of the flow between conical surfaces are found by using the method of iterative approximate solution when the inertia terms of the Navier-Stokes equations in conical coordinates are taken into account. Furthermore, we compare the centrifugal flow with the centripetal flow of axisymmetrical passing flow.
TL;DR: In this article, a modified Paris expression of fatigue crack growth rate is derived in terms of ΔK and crack angle β0 for an inclined crack, which is more convenient to express the Paris equation by means of crack length projected on the x-axis, ax rather than the actual length, a itself.
Abstract: Mixed model fatigue crack propagation is analyzed in this paper, using a centre cracked plate geometry, loaded under uniaxial cyclic tension. Based on maximum principal stress criterion, a modified Paris expression of fatigue crack growth rate is derived in terms of ΔK and crack angle β0 for an inclined crack. It is also shown that it is more convenient to express the Paris equation by means of crack lengthprojected on the x—axis, ax rather than the actual length, a itself. The crack trajectory due to cyclic loading is predicted. β0 is varied from 29° to 90°. Experimental data on Type L3 aluminium agree fairly well with predicted values when β0 exceeds 30°.
TL;DR: In this article, the fundamental equations of axisymmetric problems of ideal plasticity were reduced to two nonlinear partical differential equations, and the compatibility of Harr-Karman hypothesis with von Mises yield criterion and the associated flow law was discussed.
Abstract: In this paper, introducing a velocity potential, we reduce the fundamental equations of axisymmetric problems of ideal plasticity to two nonlinear partical differential equations. From these equations we discuss compatibility of Harr-Karman hypothesis with von Mises yield criterion and the associated flow law.
TL;DR: In this paper, simple proofs of Cayley-Hamilton theorem and l'Hopital representation theorems concerning tensor functions of an arbitrary second-order tensor are given.
Abstract: In this paper two simple proofs of Cayley-Hamilton theorem are given and by use of Cayley-Hamilton and l'Hopital's two representation theorems concerning tensor functions of an arbitrary second-order tensor are given.
TL;DR: In this article, B. Golubef method is used for calculating the radial diffuse flow between two parallel disks for the first step, and the expression of secondary approximation explicit function in which the channel length of entrance region varies with the boundary layer thickness is obtained by using Picard iteration in the solution of the energy integral equation.
Abstract: In this paper, B. B. Golubef method[1] is used for calculating the radial diffuse flow between two parallel disks for the first step. The momentum integral equation together with the energy integral equation is derived from the boundary layer momentum equation, and the expression of secondary approximation explicit function in which the channel length of entrance region varies with the boundary layer thickness can be obtained by using Picard iteration[2] in the solution of the energy integral equation. Therefore, this has made it possible to analyze directly and analytically the coefficients of the entrance region effect. In particular, when the outer diameter of disk is smaller than the entrance region length, the advantage of this method can be prominently manifest.
TL;DR: In this article, the authors describe an efficient calculation procedure for determining the interaction of vertical axisymmetric structures with the surrounding ocean, including wave forces and runup for a fixed structure, added mass and damping coefficients for an oscillating structure, and earthquake loading in terms of base shear and overturning moment.
Abstract: Vertical axisymmetric structures have found a variety of applications in offshore engineering, including oil storage tanks, production platforms and so on. The present paper describes an efficient calculation procedure for determining the interaction of such structures with the surrounding ocean. In particular, numerical calculations are explicated for:
- wave forces and runup for a fixed structure,
- added-mass and damping coefficients for an oscillating structure,
- earthquake loading in terms of base shear and overturning moment,
- motions of a floating structure.
TL;DR: In this article, the necessary and sufficient condition of uniformly convergent difference scheme for the elliptic-parabolic partial differential equation with a small parameter was studied, and the necessary condition was shown to be satisfied.
Abstract: This paper studies the necessary and sufficient condition of uniformly convergent difference scheme for the elliptic-parabolic partial differential equation with a small parameter.