Showing papers in "Applied Mathematics and Mechanics-english Edition in 1983"
TL;DR: In this paper, it is shown that the stationary conditions of these functionals give these undetermined Lagrange multipliers in terms of original variables, and the substitutions of these results for Lagrangians into the above functionals lead to the functionals of these non-conditional variation principles.
Abstract: It is known[1] that the minimum principles of potential energy and complementary energy are the conditional variation principles under respective conditions of constraints. By means of the method of Lagrange multipliers, we are able to reduce the functionals of conditional variation principles to new functionals of non-conditional variation principles. This method can be described as follows: Multiply undetermined Lagrange multipliers by various constraints, and add these products to the original functionals. Considering these undetermined Lagrange multipliers and the original variables in these new functionals as independent variables of variation, we can see that the stationary conditions of these functionals give these undetermined Lagrange multipliers in terms of original variables. The substitutions of these results for Lagrange multipliers into the above functionals lead to the functionals of these non-conditional variation principles.
65 citations
TL;DR: In this article, the distribution of shearing and normal stresses on the contact surface of the two strips composing a thermostat is found in closed form, and they are of local type and concentrated near the ends of the strip along a length almost equal to the thickness of the surface.
Abstract: The distribution of shearing and normal stresses on the contact surface of the two strips composing a thermostat is found in closed form. They are of local type and concentrated near the ends of the strip along a length almost equal to the thickness of the strip.
32 citations
TL;DR: By means of the perturbation method, a solution for large deflection of clamped circular plate under uniform pressure together with a concentrated load at the center is presented in this paper, where a load distribution function is introduced so as to make the compound loads depend on a single load parameter.
Abstract: By means of the perturbation method, this paper presents an approximate solution for large deflection of clamped circular plate under uniform pressure together with a concentrated load at the center. The special case of vanishing central deflection is also discussed. In this paper, a load distribution function is introduced so as to make the compound loads depend on a single load parameter, and average angular deflection is used as the single displacement perturbation parameter.
30 citations
TL;DR: In this article, the stability of rotational motion of a rigid body with a liquid filled cavity and a fixed point is investigated without any approximation, and the region of stability is found out explicitly.
Abstract: In this paper the problem of the stability of rotational motion of a rigid body which has a liquid filled cavity and a fixed point is investigated without any approximation. Criteria of stability and instability under finite disturbance are obtained. The region of stability is found out explicitly.
20 citations
TL;DR: In this paper, the authors investigate the distribution of steady motions of the liquid-filled-cavity body, decide the stability of each stoady motion and find out the corresponding regions of stability and instability.
Abstract: This paper is a continuation of [1]. In this paper we investigate the distribution of steady motions of the liquid-filled-cavity body, decide the stability of each stoady motion and find out the corresponding regions of stability and instability. Besides, the behaviour of disturbed motion is analysed qualitatively.
17 citations
TL;DR: In this paper, the linear exact solution and nonlinear solution for U-shaped bellows have been obtained by using the general solution of circular ring shell and the method of perturbation.
Abstract: In this paper, the linear exact solution and nonlinear solution for U-shaped bellows have been obtained by using the general solution of circular ring shell[1] and the method of perturbation.
17 citations
TL;DR: In this article, the line source and cylindrical plane source solutions of unsteady axisymmetrical two-dimensional flow through infinite and finite reservoirs with triple porosity were obtained.
Abstract: This paper seeks for the line source and cylindrical plane source solutions of unsteady axisymmetrical two-dimensional flow through infinite and finite reservoirs with triple porosity. They not only reveal the essential characteristics of fractured reservoirs but also generalize and develop the existing primal results of homogeneous and porous media.
14 citations
TL;DR: Direct numerical integration can be used to find the periodic solutions for the equations of motion of nonlinear vibration systems as discussed by the authors, where initial conditions are iterated so that they coincide with the terminal conditions.
Abstract: Direct numerical integration can be used to find the periodic solutions for the equations of motion of nonlinear vibration systems. The initial conditions are iterated so that they coincide with the terminal conditions. The time interval of the integration (i.e., the period) and certain parameters of the equations of motion can be included in the iterations. The integration method has a variable steplength.
13 citations
TL;DR: The Tangential Force Method (TFM) as mentioned in this paper is a state plane method for mass point sliding on a guide rail rotating about a vertical axis with friction disregarded, which is simpler both in argumentation and calculation, especially when one resorts to the five criteria in section XIII.
Abstract: The state plane method has been used to search the singular point and to determine their equilibrium state for a mass point sliding on a guide rail rotating about a vertical axis with friction disregarded. For the same purpose, this paper presents another method which might be briefly named “The Tangential Force Method”. In contrast with the state plane method, the new method is much simpler both in argumentation and calculation, especially when one resorts to the five criteria in section XIII.
8 citations
TL;DR: In this paper, a mixed perturbation finite element method is introduced, which incorporates the advantages of the two above-mentioned methods and enables us to solve more complicated nonlinear problems with great saving in computing time.
Abstract: The perturbation method is one of the effective methods for solving problems in nonlinear continuum mechanics. It has been developed on the basis of the linear analytical solutions for the original problems. If a simple analytical solution cannot be obtained, we would encounter difficulties in applying this method to solving certain complicated nonlinear problems. The finite element method appears to be in its turn a very useful means for solving nonlinear problems, but generally it takes too much time in computation. In the present paper a mixed approach, namely, the perturbation finite element method, is introduced, which incorporates the advantages of the two above-mentioned methods and enables us to solve more complicated nonlinear problems with great saving in computing time.
8 citations
TL;DR: In this paper, a method for conformal of a two-connected region onto an annulus is presented, which is based on the Dirichlet problem and proves that the real part of the analytic function transformation should be a harmonic function satisfying certain boundary conditions.
Abstract: This paper presents a method for conformal of a two-connected region onto an annulus. The philosophy of the method is to convert the problem into a Dirichlet problem and to prove the real part of the analytic function transformation should be a harmonic function satisfying certain boundary conditions. According to the theory of harmonic function we can determine the inner radius of the annulus from the condition that the harmonic function defined in two-connected region should be single-valued. It is then easy to see that the imaginary part can directly be obtained with the aid of Cauchy-Riemann conditions. The unknown constants of integration only influence the argument of image points and can easily be derived by using the one-to-one mapping of region onto an annulus. Without loss of generality, the method can be used to conformally map other two-connected regions onto an annulus if they can be subdivided into several rectangulars. The method has been programmed for a digital computer. It is demonstrated that the method is efficient and economical. The corresponding numerical results are shown in the Table.
TL;DR: In this article, the problem of flow of slightly compressible fluids through a bounded confined "fracture-pore" medium is solved and studied thoroughly, and the essential natures of flow flow of elastic liquids through a medium with double porosity under the condition of neglecting the flow in matrix system are revealed and clarified further.
Abstract: The problem of flow of slightly compressible fluids through a bounded confined “fracture-pore” medium is solved and studied thoroughly in this paper. Some essential natures of flow of elastic liquids through a medium with double porosity under the condition of neglecting the flow in matrix system were revealed and clarified further. The method of estimating all parameters commonly interested in a bounded confined “fracture-pore” medium reservoir through a series of flow tests in wells by use of the solution obtained is presented.
TL;DR: In this article, the subregion generalized variational principle for elastic thick plates is proposed and the finite element analysis of nonconforming elements for thick plates can be formulated on the basis of this principle.
Abstract: In this paper, the subregion generalized variational principle for elastic thick plates is proposed. Its main points may be stated as follows:
1.
Each subregion may be assigned arbitrarily as a potential region or complementary region. The subregion variational principles of potential energy, complementary energy and mixed energy represent three special forms of this principle.
2.
The number of independent variational variables in each subregion may be assigned arbitrarily. Any one of the subregions may be assigned, as a one-variable-region, two-variable-region or three-variable-region.
3.
The conjunction conditions of displacements and stresses on each interline of neighbouring subregions may be relaxed. On the basis of this principle the finite element analysis of non-conforming elements for thick plates can be formulated.
TL;DR: In this paper, the Hamilton's principle of nonholonomic variable mass systems is extended to the most general, non-holonomic, variable mass system and the Hamilton principle is illustrated with examples.
Abstract: The Hamilton's principle is extended to the most general, nonholonomic variable mass systems. The Hamilton's principle of nonholonomic variable mass systems is obtained and is illustrated with examples.
TL;DR: In this article, the authors considered the crack propagation problem in a coupled thermo-mechanical system of nonlinear media, including nonlinear elastic and elastic-plastic cases, and the related pathindependent integrals were given.
Abstract: In some engineering problems, thermo-mechanical coupling is important and may not be ignored. This paper deals with the crack propagation problem in a coupled thermo-mechanical system of nonlinear media. Various nonlinear media, including nonlinear elastic and elastic-plastic cases, have been considered and the related path-independent integrals are given. To explain the physical meaning of these integrals, a notched specimen has been considered, and the dynamical crack extension force in a coupled thermo-mechanical system is shown to be equal to this integral. Thus, we could consider such integrals as some nonlinear criteria for coupled thermo-mechanical fracture dynamics.
TL;DR: In this article, the large deflection equation of variable thickness circular plates is given and a cubic approximate solution is obtained by using small parameter method and revised iteration jointly by using a cubic approximation solution.
Abstract: In this paper, to begin with, the large deflection equation of variable thickness circular plates is given. By using small parameter method and revised iteration jointly a cubic approximate solution is obtained. A characteristic is also given for comparison with linear theory.
TL;DR: In this paper, the authors present the law of maximum rate of energy dissipation in hydrodynamics and also in general continuum dynamics as an addition to the classical conservation laws expressed in the equation of continuity and the equations of motion.
Abstract: This paper presents the law of maximum rate of energy dissipation in hydrodynamics and also in general continuum dynamics as an addition to the classical conservation laws expressed in the equation of continuity and the equations of motion. The corollary of the law is Belanger-Boss theorem of minimum reserved specific energy in applied hydraulics.
TL;DR: In this paper, homogenized equations for steady heat conduction in composite material cylinders with dilutely-distributed elliptic cylinders of impurities are derived, and explicit expressions for the corresponding effective heat conductivity of those which are concerned are obtained.
Abstract: In this paper, by using the two-space method, homogenized equations for steady heat conduction in the composite material cylinders with dilutely-distributed elliptic cylinders of impurities are derived, and the explicit expressions for the corresponding effective heat conductivity of those which are concerned are obtained. It is also shown that the macroscopic heat conduction is anisotropic when the cross-sections of the impurity cylinders are unidirectionally oriented and isotropic when the angular distribution of the cross-sections is uniform.
TL;DR: In this article, a generalized variational principle involving conditions of the rigid-plastic interface and the discontinuous surface of a velocity field has been advanced for the mixed-boundary value problem.
Abstract: This paper studies the bounding problems of the complete solution of limit analysis for a rigid-perfectly plastic medium, allowing for the discontinuity of plastic flow. A generalized variational principle involving conditions of the rigid-plastic interface and the discontinuous surface of a velocity field has been advanced for the mixed-boundary value problem. Based on this principle, a set of variational formulae of limit analysis is established. The safety factors obtained by these formulae lie between the upper and lower bounds obtained by the classical bounding theorems with the same kinematically and statically admissible field.
TL;DR: In this paper, a so far unknown explicit expression for the rate of the right stretch tensor is offered in absolute notation, and two ways of defining objective stress-rates are presented.
Abstract: Presenting some recent considerations and results, the present paper deals with two basic concepts of the continuum mechanics: strain-and stress-rates. Upon a brief systematic survey of concepts of strain and stress, a so far unknown explicit expression for the rate of the right stretch tensor is offered in absolute notation. This paper then suggests to distinguish two ways of defining objective stress-rates. Following the second procedure, after analyzing several particular cases, the author proposes a generalized Jaumann flux, which contains the majority of the existing definitions for stress-rate and the Hill's result as well.
TL;DR: In this article, both the Lyapunov stability and Popov's hyperstability of discrete linear time-invariant systems in case of system parameter disturbance are discussed.
Abstract: Both the Lyapunov stability and Popov's hyperstability of discrete linear time-invariant system in case of system parameter disturbance are discussed in this paper. The allowable disturbance ranges are given so that the maintenance of the Lyapunov stability and the Popov's hyperstability of a discrete linear system is guaranteed. The results find their significance in the MRAC.
TL;DR: In this paper, the propagation of a long wave in a three-dimensional curved duct with variable cross section is studied and the influences of the duct's geometric parameters (the area variation of the cross section, the curvature and torsion of the central line) on the asymptotic expansion of the solution are analyzed.
Abstract: The propagation of a long wave in a three-dimensional curved duct with variable cross section is studied in this paper. It is shown that a three-dimensional Helmholtz equation can be decomposed into a two-dimensional Laplace (or Poisson) equation and a one-dimensional Webster equation by the curvilinear orthogonal coordinate system, non-dimensionization of reduced wave equation and regular perturbation with small parameterka, wherek is the wave number anda is the characteristic radius of the duct. The influences of the duct's geometric parameters (the area variation of the cross section, the curvature and torsion of the central line) on the asymptotic expansion of the solution are analysed. It is concluded that the effects of the variation of the cross sectional area first appear in the first term of the asymptotic expansion, and when the cross section shape has certain symmetric properties, the effects of the curvature and torsion of the central line first appear in the third and the fourth terms, respectively. An example of long wave propagation in a curved circular duct is also given at the end of this paper.
TL;DR: In this article, a rectangular plate is considered and its opposite edges are simply supported, while the other two are arbitrary, and the rigidity of the plate is variable along the direction parallel to the simply supported edges.
Abstract: The subject discussed in this paper is the rectangular plate. Its wwo opposite edges are simply supported, while the other two are arbitrary, and the rigidity of the plate is variable along the direction parallel to the simply supported edges. In order to solve the problem, the author adopts the finite plate-strip element method[1], which is different from the usual finite element method or the finite strip method. The steps of the above method is no longer to establish a rigidity matrix for elements or strips and gather them into a total matrix for solution. Now the relation of transfer between the strain and inner force of every plate-strip is shown. Finally a practical example is given and this method is found to be easier and more effective.
TL;DR: Different kinds of modal synthesis method have been used widely in dynamic analysis of linear structure systems, but, in general, they are not suitable for nonlinear systems as discussed by the authors. But, in this paper, we focus on nonlinear structure systems.
Abstract: Different kinds of modal synthesis method have been used widely in dynamic analysis of linear structure systems, but, in general, they are not suitable for nonlinear systems.
TL;DR: In this article, the authors considered the problem of an infinite plane with a circular hole welded by a nearly circular plate with a crack of different material and transformed the problem into a certain boundary value problem of analytic functions and then reduced to solving a singular integral equation along the crack.
Abstract: In this paper, the problem of an infinite plane with a circular hole welded by a nearly circular plate with a crack of different material is considered. The problem is transformed into solving a certain boundary value problem of analytic functions and then reduced to solving a singular integral equation along the crack. The formulas and some numerical results of the factors of stress intensity for the cases Mode I and Mode II are obtained at the end of this paper.
TL;DR: In this article, the Fourier expansions upon the system of orthonormal polynomials are used to obtain the expressions of displacements as well as stresses directly from the solutions, and based on the principle of virtual work the equilibrium equations of various orders are formulated.
Abstract: In order to formulate the equations for the study here, the Fourier expansions upon the system of orthonormal polynomials are used. It may be considerably convenient to obtain the expressions of displacements as well as stresses directly from the solutions. Based on the principle of virtual work the equilibrium equations of various orders are formulated. In particular, the system of thirdorder is given in detail, thus providing the reference for accuracy analysis of lower-order equations. A theorem about the differentiation of Legendre series term by term is proved as the basis of mathematical analysis. Therefore the functions used are specified and the analysis rendered is no longer a formal one. The analysis will show that the Kirchhoff-Love's theory is merely of the first-order and the theory which includes the transverse deformation but keeps the normal straight is essentially of the first order, too.
TL;DR: In this article, the cavitation conditions and similarity problems are discussed with thermodynamic effects taken into consideration in addition to the hydrodynamic ones, which is suitable for discussing expansior or contraction motion of a bubble formed in liquid, but this theory does not cope with cavitation behaviors in general.
Abstract: Many studies on cavitation phenomena were based on the theory of single bubble motion which was first put forward by Rayleigh in his 1917 article and later developed by Plesset et al.[1]. By this theory, only some effects of forces were taken into consideration from hydrodynamics leaving out any thermodynamical effects such as matter interchange between liquid and gaseous phases. Strictly speaking, the theory may be suitable for discussing expansior or/and contraction motion of a bubble formed in liquid, but this theory does not cope with cavitation behaviors in general. In this paper, the cavitation conditions and similarity problems are discussed with thermodynamic effects taken into consideration in addition to the hydrodynamic ones.
TL;DR: In this article, the problem of non-Newtonian oil displacement by water in porous media, adopting the linear permeation law with initial pressure gradient, was considered and numerical solutions were obtained.
Abstract: This paper considers the problem of non-Newtonian oil displacement by water in porous media, adopting the linear permeation law with initial pressure gradient. For one-dimensional flow, the basic equation of non-Newtonian oil displacement by water in sandstone reservoirs and fractured reservirs is derived and numerical solutions are obtained. The results are compared with the corresponding ones for Newtonian oil displacement to show the essential characteristics of non-Newtonian oil displacement by water.
TL;DR: In this article, a multi-valued displacement problem for an eccentric circular ring is considered and the general expression of stress function is derived in the bipolar coordinate system and its application is explained.
Abstract: In this paper, by using N. I. Muskhelishvili's method a multi-valued displacement problem is considered for an eccentric circular ring. The general expression of stress function is derived in the bipolar coordinate system and its application is explained.