应用数学和力学

1992 Vol. 13, No. 12

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Hamiltonian System and Simpletic Geometry in Mechanics of Composite Materials(Ⅱ)--Plane Stress Problem

Zhong Wan-xie, Ouyang Hua-jiang

1992, 13(12): 1031-1035.

Abstract(2521) PDF(635)

Abstract:
The fundamental theory presented in part(I)^[8] is used to analyze anisotropic plane stress problems.First we construct the generalized variational principle to enter Hamiltonian system and get Hamiltonian differential operator matrix;then we solve eigen problem;finally,we present the process of obtaining analytical solutions and semi-analytical solutions for anisotropic plane stress porblems on rectangular area.

Numerical Solution of a Singularly Perturbed Elliptic Hyperbolic Partial Differential Equation on a Nonuniform Discretization Mesh

Wu Qi-guang, Sun Xiao-di

1992, 13(12): 1037-1044.

Abstract(2167) PDF(622)

Abstract:
In this paper,we consider the upwind difference scheme for singular perturbation problem(1.1).On a special discretization mesh,it is proved that the solution of the upwind difference scheme is first order convergent,uniformly in the small parameter ε,to the solution of problem(1.1).Numerical results are finally provided.

Finite-Part Integral and Boundary Element Method to Solve Flat Crack Problems

Qin Tai-yan, Tang Ren-ji

1992, 13(12): 1045-1051.

Abstract(2112) PDF(684)

Abstract:
Using the Somigliana formula and the concepts of finite-part integral,a set of hypersingular integral equations to solve the arbitrary flat crack in three-dimensional elasticity is derived and its numerical method is then proposed by combining the finite-part integral method with boundary element method.In order to verify the method,several numerical examples are carried out.The results of the displacement discontinuities of the crack surface and the stress intensity factors at the crack front are in good agrement with the theoretical solutions.

Model B-l for Macro Rectangular Element and Problems of Influence Surface for Plate Structures

Wang Jin-zhong, He Chang-hua

1992, 13(12): 1053-1060.

Abstract(2082) PDF(643)

Abstract:
Model B-I for marco rectangular element is presented for the first time in this paper.To establish the influence surf ace for resultant R of bending plates,a number of generalized distributive loads q are defined.It is shown by numerical examples that Model B-I and the formula for the generalized distributive loads advanced in this paper are featured by high accuracy,low memory space and flexibility in practical application,and that they are especially effective for plate structures subject to moving loads,such as the two-dimensional continuous plates of highway bridges and the flat stabs in piled jetty engineering.

Mixed Finite Element Method of Hexahedral Elements for Navier-Stokes Problem

Luo Zhen-dong

1992, 13(12): 1061-1067.

Abstract(1823) PDF(619)

Abstract:
In this paper,we derive a new mixed element format of hexahedral elements for Navier-Stokes problem in three-dimensional space.

The Explicit Solution of Homogeneous Linear Ordinary Differential Equations with Constant Coefficients

Huang Yong-nian

1992, 13(12): 1069-1074.

Abstract(1990) PDF(838)

Abstract:
In this paper by using tensor analysis we give the explicit expressions of the solution of the initial-value problem of homogeneous linear differential equations with constant coefficients and the nth-order homogeneous linear differential equation with constant coefficients.In fact,we give the general formula for calculating the elements of the matrix e^At.We also give the results when the characteristic equation has the repeated roots.The present method is simpler and better than the other methods.

The New Solution for the Axially Symmetrical Laminar Boundary Layer Equations between Two Parallelf Spherical Surfaces

Ding Zhong-man, Wang Zhi-qing

1992, 13(12): 1075-1080.

Abstract(1887) PDF(667)

Abstract:
The transformations,which are similar to Mangler's transformations,are given in this paper.They change the entrance region flow of axially symmetrical laminar boundary layer between two parallel spherical surfaces into the flow of two-dimensional boundary layer,and simplify the problems.The simplified equations can be solved by the two-dimensional boundary layer theory and numerical methods.Therefore,a new way is opened up to solve the diffusive laminar flow in the entrance region between two parallel spherical surfaces.

A Method Using the Reciprocal Theorem to Solve the Bending of Thin Elastic Semicircular Plates

Li Nong

1992, 13(12): 1081-1085.

Abstract(1883) PDF(798)

Abstract:
The bending of the thin elastic semicircular plates,because of its complicated boundary conditions,brings some difficulties for us to obtain its solution.This paper applies the reciprocal theorem to propose a general simple convenient method to obtain the transverse deflectional equations of the plates.

The Polynomial Stress Function Solution for the Rectangular Strip Bending

Yuan Yi-wu

1992, 13(12): 1087-1095.

Abstract(1822) PDF(631)

Abstract:
In this paper,we propose some formulas for seeking a part of the particular solutions of the heavy harmonics and Tricomi equations and obtain the precise polynomial solutions of the finite-item number for rectangular strip bending problem when the intensity of the distributed load varies with the fourth power of longitudinal coordinate.

Effect of Skin Friction on the Directional Stability of Driven Piles during Driving

Shen Xi-ying, Gao Da-zhao

1992, 13(12): 1097-1102.

Abstract(2168) PDF(711)

Abstract:
In this paper,the driving forces at a pile top are considered as a periodic load during driving and the Mathieu equation is derived.From the stability charts of this equation,we can obtain the critical length of the pile,and the effect of skin friction upon the critical length is discussed.

Nonsymmetrical Large Deformation Bending Problem of Circular Thin Plates

Wang Lin-xiang, Wang Xin-zhi, Qiu Ping

1992, 13(12): 1103-1116.

Abstract(2106) PDF(682)

Abstract:
To begin with,in this paper,the displacement governing equations and the boundary conditions of nonsymmetrical large deflection problem of circular thin plates are derived.By using the transformation and the perturbation method,the nonlinear displacement equations are linearized,and the approximate boundary value problems are obtained.As an example,the nonlinear bending problem of circular thin plates subjected to comparatively complex loads is studied.

The Elastic Solution of Concentrated Force Acting in Orthogonal Anisotropic Half-Plane and Constant Element Fundamental Formulae of Boundary Element Method

Wen Pi-hua

1992, 13(12): 1117-1126.

Abstract(2363) PDF(796)

Abstract:
In this paper,the elastic solutions of concentrated force acting in orthogonal anisotropic half-plane are derived by imaginal method and the formulae of coefficient matrix for constant element are put forward.To solve half-plane problems numerically by BEM,this paper provides the necessary formulae.Because the expressions of fundamental solutions are very simple,the object functions could be obtained for every integral of constant element and higher order element of indirect BEM.Thus,the procedure of integration could be avoided in calculation program