应用数学和力学

1990 Vol. 11, No. 6

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A Penalty-Hybrid Finite Element Analysis of Stokes Flow

Chen Da-peng, Zhao Zhong

1990, 11(6): 467-476.

Abstract(1674) PDF(432)

Abstract:
A type of penalty-hybrid variational principle is suggested for the analysis of Stokesian flow. On such a basis, a finite element model is formulated featuring, among others, a priori satisfaction of the deviatoric stress and hydrostatic pressure on linear momentum balance equations. Also in the present scheme the hydrostatic pressure is successfully eliminated at the element level, leaving only nodal velocities as solution unknowns. A series of 4-node and 8-node quadrilateral elements are derived and examined. Numerical examples demonstrating their characteristic behaviors are also included.

The Mixing of Gas-Liquid Flow with Vapor and Gas Solid Flow

Lin Duo-min, Tsai Shu-tang

1990, 11(6): 477-482.

Abstract(1806) PDF(473)

Abstract:
In the industrial production, the mixing of gas-liquid flow with vapor and gas-solid flow is a very common problem. In the process of the mixing, solid particle-clusters will form, and will have steady radii when the effect of the gathering of particles is balanced withthat of the breaking of particle-clusters. Then, the population distribution function n(a,,t) of size of particles per unit length per unit volume is introduced, and its governingequation is derived on the analogy of the molecular kinetic theory. Finally, when the gas flow is very slow, the expression of steady average radius of particle-clusters is obtained.

Generalized Strongly Nonlinear Quasi-Complementarity Problems in Hilbert Spaces

Zhang Shi-sheng, Huang Nan-jing

1990, 11(6): 483-488.

Abstract(1585) PDF(452)

Abstract:
In this paper, we introduce a new kind of generalized strongly nonlinear quasi-complementarity problems in Hilbert space and discuss the existence of solutions for this kind of problems and the convergence of sequences generated by algorithms. The results presented in this paper improve and extend a number of known results.

Torsion of Elastic Shaft of Revolution Embedded in an Elastic Half Space

Yua Tian-quan

1990, 11(6): 489-498.

Abstract(2027) PDF(472)

Abstract:
The problem of torsion of elastic shaft of revolution embedded in an elastic half space is studied by the Line-Loaded Integral Equation Method (LLIEM). The problem is reduced to a pair of one-dimensional Fredholm integral equations of the first kind due to the distributions of the fictitious loads "Point Ring Couple (PRC)"and "Point Ring Couple in Half Space (PRCHS)"on the axis of symmetry in the interior and external ranges of the shaft occutied respectively. The direct discrete solution of this integral equations may be unstable, i.e. an ill-posed case occurs. In this paper, such an ill-posed Fredholm integral equation of first kind is replaced by a Fredholm integral equation of the second kind with small parameter, which provides a stable solution. This method is simpler and easier to carry out on a computer than the Tikhonov's regularization method for ill-posed problems. Numerical examples for conical, cylindrical, conical-cylindrical, and parabolic shafts are given.

A Fuzzy Model for the Failure of Composite Structures

Pan Jing-zhe, Luo Zu-dao

1990, 11(6): 499-504.

Abstract(1680) PDF(534)

Abstract:
In this paper, the fuzzy theory is used to describe the uncertainty in failure definition of composite structures. The concept of structural failure level (SFL) is suggested and a method of evaluation is presented.

The Bending of a Thick Rectangular Plate with Three Clamped Edges and One Free Edge

Cheng Chang-jun, Yang Xiao

1990, 11(6): 505-520.

Abstract(1749) PDF(696)

Abstract:
The exact solution of the bending of a thick rectangular plate with three clamped edges and one free edge under a uniform transverse load is obtained by means of the concept of generalized simply-supported boundary^[1] in Reissner's theory of thick plates. The effect of the thickness h of a plate on the bending is studied and the applicable range of Kirchhoffs theory for bending of thin plates is considered.

Several Classes of Integrable Nonlinear Ordinary Differential Equations (Ⅱ)——Higher-Order Equations

Li Hong-xiang

1990, 11(6): 521-527.

Abstract(1829) PDF(567)

Abstract:
In this paper, several classes of integrable nonlinear higher-order ordinary differential equations are given. It is pointed out that some known results of integrability or integrable equations are all special cases of them. These equations have a wide-ranging applied background in physics and mechanics.

Generalized Whittaker Equations and Field Method in Generalized Classical Mechanics

Mei Feng-xiang

1990, 11(6): 529-536.

Abstract(1966) PDF(515)

Abstract:
This paper presents the energy integral in generalized classical mechanics. The integral enables us to reduce a given canonical system with 2n order to another system with only (2n-2) order and to obtain generalized Whittaker equations. And then, this paper extends a field method integrating the equations of motion for classical mechanics to generalized dassical mechanics. Finally, this paper gives an example to illustrate the application of these equations and the field method.

Transversely Isotropic Beam under Enitial Stress

Wang Jin-ying, Lü Zhong-da

1990, 11(6): 537-646.

Abstract(1817) PDF(478)

Abstract:
Starling from Novozhilov's nonlinear equations of elasticity by appropriate simplification and integration over the beam cross-section, a linearized set of equations for a transversely isotropic beam under initial non-uniform state of stress is obtained. In the absence of initial stress, the obtained equations are reduced to well-known Timoshenko beam equations.These equations are applied to investigate the vibration and buckling characteristics of a transversely isotropic beam under uniform initial axial force and bending moment.

The Size Effect on the Dispersion of a Particle in a Homogeneous Isotropic Turbulence

Xie Ding-guo

1990, 11(6): 547-554.

Abstract(1773) PDF(500)

Abstract:
The mechanism of the response motion of a suspended particle to turbulent motion of its surrounding fluid is different according to size of turbulent eddies. The particle is dragged by the viscous force of large eddies, and meanwhile driven randomly by small eddies. Based on this understanding, the dispersion of a particle with finite size in a homogeneous isotropic turbulence is calculated in this study. Results show that there are two competing effects: when enhanced by the inertia of a particle, the long-term particle diffusivity is reduced by the finite size of the particle.

On J Integrals in the Plane Fracture

Yang Wei-yang, Zhang Shao-qin, Chen Hua-cai

1990, 11(6): 555-564.

Abstract(1846) PDF(776)

Abstract:
In this paper, we discuss J-integrals near models Ⅰ and Ⅱ crack tips for the plates of linear-elastic isotropic homogeneous material and orthotropic composite material, using the theories of complex function and calculus, and obtain the result as follows:(1) The various J-integrals are transformed into standard form of line integrals with respect to coordinates: J=∫_rp(x,y)dx+Q(x,y)dy (2) Independence of path of the various J-integrals is proved.(3) Computing formulae of J-integrals are derived.