Applied Mathematics and Mechanics (English Edition)

GENERALIZED PLASTICITY AND SOME MODELS FOR GEOMECHANICS

O.C.Zienkiewicz

1982, 3(3): 303-318.

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In this brief note, we have (a) introduced a very general form of plasticity definition; (b) indicated several types of models used for monotonic and transient loading of soil-like materials, which do not depend on time effects. The details of each form are given elsewhere but we believe that the new framework provides an easier and more general interpretation of a variety of behaviour form.

DYNAMIC FINITE ELEMENT WITH DIAGONALIZED CONSISTENT MASS MATRIX AND ELASTIC-PLASTIC IMPACT CALCULATION

钱伟长

1982, 3(3): 319-334.

摘要 ( 456 )

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There are some common difficulties encountered in elastic-plastic impact codes such as EPIC^[1,2] NONSAp^[3] etc. Most of these codes use the simple linear functions usually taken from static problems to represent the displacement components. In such finite element formulation, the strain and stress components are constants in every element. In the equations of motion, the stress components in general appear in the form of their space derivatives. Thus, if we use such form functions to represent the displacement components, the effeffb. of internal stresses to the equations of motion vanishes identically. The usual practice to overcome such difficulties is to establish as self-equilibrium system of internal forces acting on various nodal points by means of transforming equations of motion into variational form of energy relation through the application of virtual displacement principle. The nodal acceleration.is then calculated from the total force acting on this node from all the neighbouring elements. The transformation of virtual displacement principle into the variational energy form is performed on the bases of continuity conditions of stress and displacement throughout the integrated space. That is to say, on the interface boundary of finite element, the assumed displacement and stress functions should be conformed. However, it is easily seen that, for linear form function of finite element calculation, the displacement continues everywhere, but not the stress components. Thus, the convergence of such kind of finite element computation is open to question. This kind of treatment has never been justified even in approximation sense. Furthermore, the calculation of nodal points needs a rule to calculate the mass matrix. There are two ways to establish mass matrix, namely lumped mass method and consistent mass methodt4J. The consistent mass matrix can be obtained naturally through finite element formulation, which is consistent to the assumed form functions. However, the resulting consistent mass matrix is not in dia-gonalized form, which is inconvenient for numerical computation. For most codes, the lumped mass matrix is used, and in this case, the element mass is distributed in certain assumed proportions to all the nodal points of this element. The lumped mass matrix is diagonalized with diagonal terms composed of the nodal mass. However, the lumped mass assumption has never been justified. All these difficulties are originated from the simple linear form functions usually used in static problems. In this paper, we introduce a new quadratic form function for elastic-plastic impact problems. This quadratic form function possesses diagonalized consistent masf matrix, and non-vanishing effect of internal stress to the equations of motion. Thus with this kind of dynamic finite element, all above-said difficulties can be eliminated.

ON PATH-INDEPENDENT INTEGRALS AND FRACTURE CRITERIA IN NONLINEAR FRACTURE DYNAMICS

欧阳鬯

1982, 3(3): 335-343.

摘要 ( 480 )

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In this paper, we consider path-independent integrals and fracture criteria in nonlinear fracture dynamics. The dynamic effect and crack propagation are included in the discussion. Both nonlinear elastic and elastic-plastic case for crack propagation have been considered, and the related path-independent integrals are proposed. As an example, the steady state propagation of crack has been discussed. Lastly, we give the mechanical meaning of this path-independent integrals as the crack extension force, and make it possible to use the path-independent integrals (as fracture criterion in nonlinear fracture dynamics).

FREE CONVECTION FLOW OF WATER AT 4℃ PASSING AN INFINITE POROUS PLATE WITH CONSTANT SUCTION IN A ROTATING SYSTEM

A.Raptis;C.Perdikis;G.Tjivanidis

1982, 3(3): 345-351.

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In this work an analysis of steady free convection flow of water at 4℃ passing a vertical infinite porous plate in a rotating system is considered. Approximate solutions for the coupled nonlinear equations are obtained for the velocity and the temperature. The effect of E’ (Eckman number) is discussed, when P (prandtl number)=11.4, which corresponds to water at 4℃.

APPLICATIONS OF THE RECIPROCAL THEOREM TO SOLVING THE EQUATIONS OF THE DEFLECTION SURFACE OF THE RECTANGULAR PLATES WITH VARIOUS EDGE CONDITIONS

付宝连

1982, 3(3): 353-364.

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This paper points out that on certain condition the reciprocal theorem is equivalent to the superposition principle of displacements. On the basis of [6], applications of the reciprocal theorem are further extended; a convenient, general and new method for solving the equations of deflection surface of the rectangular plates and the straight beams with various edge conditions under various loads is pie-sented.

THE FLOQUET THEORY FOR QUASI-PERIODIC LINEAR SYSTEMS

林振声

1982, 3(3): 365-381.

摘要 ( 418 )

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In this paper we establish the Floguet theory for the quasi-periodic system

where A(u₁,u₂....u_m) is an nxn periodic matrix function ofwith period 2π, and it is of C^τ, τ=(N+ 1)τ₀, τ₀=2(m + 1), N = (1/2)n(n + l).Meanwhile, we define the characteristic exponential roots β₁,β₂,…,β_n of (0.1), and assume that

where K(ω), K(ω,β)->0. k_u, i_v, are integers, all the integers k₁,k₂,…,k_m,k_m are not zero,,

,rhen therequasi-periodic linear transformation, which carries (0.1) into a li near system with constant coefficients.

RANDOM FIXED POINT THEOREMS FOR COMMUTING RANDOM OPERATORS IN PROBABILISTIC FUNCTIONAL ANALYSIS

张石生

1982, 3(3): 383-392.

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Random fixed point theorems are of fundamental importance in probabilistic functional analysis. In complete separable metric space random fixed point theorems have been discussed by Bharucha-Reidf1/27, Hans[3], Itohf4,5J and the author’s papers[15-20].In this paper we obtain a random fixed point theorem for commuting random operators in probabilistic functional analysis. Our results generalize some important results also extend and unify some results in Jungck[6,7,8]t Das and Naiki[9] as well as Bhoades[10] adn ciric[11].

THE REGION OF POSSIBLE MOTION OF THE PLANAR CIRCULAR RESTRICTED THREE-BODY PROBLEM UNDER THE INFLUENCE OF A RING

张翔龄

1982, 3(3): 393-404.

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This paper discusses the region of possible motion of planar circular restricted three-body problem that one primary in them has a ring and it gives the equation of motion of the third body. Some results, are as follows:(1) The location of equilibrium points depends on the parameter n of the system; inner radius a and outer radius b of the ring; the distance I between two primaries; and the ratio 9 of the mass of the ring with the sum of masses of the primary which has the ring and the ring itself. When a, b, l, B are constant, the number of the equilibrium points varies with d, it is five at most and three at least. Besides each triangular point and two primaries form an isosceles triangle.(2) When a, b, l, 6 are constant, we give a range of μ. If μ is in this range, the structure of the region of possible motion of the third body is the same as that of general planar circular restricted three-body problem.

LOAD CAPACITY OF OILFILM——LUBRICATED BALL-BEARING WITH SPIRAL GROOVES

阚健民;朱月锐

1982, 3(3): 405-418.

摘要 ( 436 )

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Jn order to improve load capacity and stability of a fluid moving-pressure bearing, at present, measure of cutting grooves on a turning-shaft is generally adopted.The performances of spiral grooves are better in various groove-types. Therefore, a theoretical analysis and an experimental investigation of the bearing with spiral grooves attract general attention. But the results of most articles published in china are numerical solutions of the computer. Using the methods of parameter perturbatiqn in the paper, an approaching analytical solution of Reynolds equation of the moving-pressure oil film-lubricated ball-bearing with spiral grooves has been obtained. We have combined the numerical solutions of the computer, and the influence of the bearing parameters upon the load capacity is discussed; the optimum values of the groove parameter are obtained. The theoretical conclusion of this paper is in good agreement with the experimental data obtained by "651" Institute.

THE PROPERTIES AND APPLICATIONS OF THE INTEGRATING FACTOR IN THE QUALITATIVE THEORY OF ORDINARY DIFFERENTIAL EQUATIONS

李骊

1982, 3(3): 419-431.

摘要 ( 527 )

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In this article, we indicated that all the problems, such as the classification of the singular point and the determination of the stability of limit cycle, can be solved by the application of the integral factor. Especially we gave a criterion for deciding the center and the focus, which is appropriate for the singular point of the first order as well as that of the higher order.In the qualitative theory of ordinary differential equations,all the problems, such as the classification of singular point of the first order and higher order, and the determination of stability of limit cycle, are important problems to be solved by different ways, the distinction between a focus and a center of singular point of the higher order is an unsolved problem. In this paper, we show that all the problems mentioned above can be solved by the use of the integrating factor. A criterion is given to decide the center and the focus, and this criterion is applicable to the singular point of the first order as well as the higher order.

STUDY ON CORRECTION COEFFICIENTS OF LIMINAR AND TURBULENT ENTRANCE REGION EFFECT IN ROUND PIPE

王致清

1982, 3(3): 433-446.

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In this paper, a universal method for calculation of the inlet length and correction coefficient for the pressure losses and the flow in the case of laminar and turbulent flow in a smooth round pipe is put forward.With the aid of concrete examples, theoretical formulas are presented for calculation of the correction coefficient for pressure losses and flow in the case of laminar and turbulent flow. And a method for calculation of the flow is also presented here in consideration of the inlet effect of turbulent flow.By comparing the theoretical results with the experimental data, formulas presented in this paper are very simple and reliable.

THE DISTRIBUTION OF THE SPECIFIC PRESSURE IN ROLLING STRIPS

刘培锷;刘证

1982, 3(3): 447-455.

摘要 ( 356 )

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The principle of the distribution of the specific pressure in rolling strips is used not only for calculating the total rolling pressure but also for providing the basis in calculating the widening and in designing the rational roll profile. Hitherto, the results of analysis on this subject in the references are expressed as a function of one dimension, and they cannot reflect the variation of the specific pressure along the width of the contact surface. This paper deals with the two-dimensional expression of the principle.of the distribution of the specific pressure with the help of the calculus of variations.

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