应用数学和力学

A Closed System of Equations for Dense Two-Phase Flow and Expressions of Shearing Stress of Dispersed Phase at a Wall

Lin Duo-min, Cai Shu-tang

1989, 10(8): 649-656.

Abstract(2155) PDF(636)

Abstract:
Inthis paper, each of the two phases in dense two-phase flow is considered as continuous medium and the fundamental equations for two-phase flow arc described in Eulerian form. The generalized constitutive relation of the Bingham fluid is applied to the dispersed phase with the analysis of physical mechanism of dense two-phase flow. The shearing stress of dispersed phase at a wall is used to give a boundary condition. Then a mathematical model for dense two-phase flow is obtained. In addition, the expressions of shearing stress of dispersed phase at a wall is derived according to the fundamental model of the friclional collision between dispersed-plutse particles and the wall.

Primary Research on Subjectivity Geometry

Yun Tian-quan

1989, 10(8): 657-661.

Abstract(1998) PDF(485)

Abstract:
The so-called "Subjectivity Geometry" herein is a course for studying the relationship between the abstracted object configuration and its observed record by means of mathematical methods and described by matlieinatical language. There are many features differing from the common geometry when the effects of the subjectivity(such as the position of the observer, the functions of the visual system of human) are taken into account during the observing-recording process. In this paper, some basic assumptions are made; spherieal observing record is suggested: the fundamental relationship between the abstracted object configuration and its corresponding observed record is studied and an example of apiriication of the above theory is presented. We anticipate that the study of subjectivity geometry will influencc, or will be associated with the study of physiology of the visual system, applied optics etc., and will be useful in surveying, pilotage and imitative biology, etc.

The Improved Isoparametric Transformation in BEM

Ding Hao-jiang, He Wen-jun

1989, 10(8): 663-668.

Abstract(2006) PDF(738)

Abstract:
The so-called "Subjectivity Geometry" herein is a course for studying the relationship between the abstracted object configuration and its observed record by means of mathematical methods and described by matlieinatical language. There are many features differing from the common geometry when the effects of the subjectivity(such as the position of the observer, the functions of the visual system of human) are taken into account during the observing-recording process. In this paper, some basic assumptions are made; spherieal observing record is suggested: the fundamental relationship between the abstracted object configuration and its corresponding observed record is studied and an example of apiriication of the above theory is presented. We anticipate that the study of subjectivity geometry will influencc, or will be associated with the study of physiology of the visual system, applied optics etc., and will be useful in surveying, pilotage and imitative biology, etc.

Two Dimensional Stress Wave Analysis in Incompressible Elastic Solids

Tang Zhi-jing, T. C. T. Ting, Li Yong-chi

1989, 10(8): 669-678.

Abstract(2688) PDF(574)

Abstract:
Two-dimensional stress wares in n general incompressible elastic solid are investigated. First, baxic equations for simple wares and shock waves are presented for a general strain energy junction. Then the characteristic ware speeds and the associated characteristic vectors are deduced. It is shown that there usually exist two simple waves and two shock wares. Finally, two examples are given for the case of plane strain deformation and antiplane strain deformation, respectively. It is proved that, in the case of plane strain deformation, the oblique reflection problem of a plane shock is not solvable in general.

Blow-up of Solutions of Nonlinear Pseudo-Hyperbolic Equations of Generalized Nerve Conduction Type

Zhang Jian

1989, 10(8): 679-687.

Abstract(2143) PDF(684)

Abstract:
This paper deals with the two types of mixed problems with respect to Neumann boundary and Dirichlet boundary for nonlinear pseudo-hyperbolic equations of generalized nerve conduction type u_tt-Δu_t=F(x,t,u,∇u,u_t,∇u_t) when the nonlinear part F(x,t,u,∇u,u_t,∇u_t) and the initial values satisfy some conditions, the blow-up properties of the solytions are obtained.

The Increment Stiffness Matrix and Total Quantum Stiffness in Nonlinear Analyses

Li Long-yuan

1989, 10(8): 689-692.

Abstract(2692) PDF(738)

Abstract:
In this paper, the expressions of both increment stiffness matrix and total quantum stiffness matrix in nonlinear analyses are derived in detail, and their relationship is discussed in mathematical meaningThe results given in our paper will be of great importance to the analyses of nonlinear numerical and nonlinear stability in finite element methods.

The Method of the Reciprocal Theorem of Forced Vibration for the Elastic Thin Rectangular Plates(Ⅰ)——Rectangular Plates with Four Clamped Edges and with Three Clamped Edges

Fu Bao-lian, Li Nong

1989, 10(8): 693-714.

Abstract(2431) PDF(615)

Abstract:
In this paper the method of the reciprocal theorem(MRT) is extended to solve the steady state responses of rectangular plater under harmonic disturbing forces. A series of the closed solutions of rectangular plates with various boundary conditions are given and the tables and figures which have practical value are provided.MRT is a simple, convenient and general method for solving the steady stale responses of rectangular plates under various harmonic disturbing forces.The paper contains three parts:(Ⅰ) rectangular plates with four damped edges and with three clamped edges;(Ⅱ) rectangular plates with two adjacent clamped edges;(Ⅲ) cantilever plates.We arc going to publish them one after another.

Vibrations of Rectangular Plates Supported at Corner Points

Cheng Xiang-sheng

1989, 10(8): 715-720.

Abstract(2166) PDF(630)

Abstract:
This paper discusses by energy theorem the methodof approximate computation for the lowest eigenfrequencies of rechmguhir plates,on which there are symmetrical concentrated masses,supported at corner points,In the case of seseral concentrated masses,by using the prineiple of superposition we mayfiml the reduneed coefficients of masses comveniently.llence we can louain the lowest eigenfrequencies of thin plates.In the paper a good mamy mmerical caleuhting eximples are illustrated.

Anisotropic Plastic Stress Fields at a Slowly Propagating Crack Tip

Lin Bai-song

1989, 10(8): 721-727.

Abstract(1895) PDF(544)

Abstract:
Under the condition that any perfeetly plastic stress components at a crack tip are nothing but the Junctions of 0 only, making use of equilibriumequations,Hill ani.sutropic yield condition and unloading stress-strain relations, in this paper, we derive the general analytical expressions of anisotropic plastiestress Jields at the slowly steadyhe slowly steady propagatin tips of plane and anti-phane strain,Applying these general analytical expressions to the concrete cracks the attchvtical expressions of anisotropie plastic stress fields at the slowly steady propagating tips of Motle I and Motle III cracks are obtained. For the isolropic plastic material, the anisotropic plastic stress fields at a slowly propagating crack tip become the perfeeby plastic mress fields.

Axisymmetric Problems of Cylindrical Shells with Variable Wall Thickness

Wang Shen-xing

1989, 10(8): 729-745.

Abstract(1771) PDF(546)

Abstract:
The purpose of this paper is to give the general solutions for axisymmetric eylindrical shells with paraholically varying wall thickness.

1989 Vol. 10, No. 8