应用数学和力学

Singular Perturbation of Boundary Value Problem for a Vector Fourth Order Nonlinear Differential Equation

Lin Zong-chi, Lin Su-rong

1988, 9(5): 385-395.

Abstract(1839) PDF(483)

Abstract:
We study the vector boundary value problem with boundary perturbations:
ε²y⁽⁴⁾=f(x,y,y″,ε,μ)(μy(x,ε,μ)|_x=μ=A₁(ε,μ),y(x,ε,μ)|_x=1-μ=B₁(ε,μ)
y″(x,ε,μ)|_x=μ=A₂(ε,μ),y″(x,ε,μ)|_x=1-μ=B₂(ε,μ)
where y f, A_j and B_j (j=1,2) are n-dimensional vector functions and ε, μ are two small positive parameters. This vector boundary value problem does not appear to have been studied, although the scalar boundary value problem has been treated. Under appropriate assumptions, using the method of differential inequalities we find a solution of the vector boundary value problem and obtain the uniformly valid asymptotic expansions.

A New Method of Stress Analysis in Photoelasticity

An Li-qian, Chen Zhi-da

1988, 9(5): 397-402.

Abstract(1725) PDF(470)

Abstract:
A new method of stress analysis in photoelasticity has been developed in this paper. Only the orders of isochromatic fringes and boundary conditions in three sections are adopted to analyse the stress components in these sections. The method requires minimum known data and can quickly analyse stress components. It reduces computational programs.

Numerical Analysis of Edge Effect in Laminated Composite Structures

Ye Bi-quan, Zhou Huan-wen

1988, 9(5): 403-410.

Abstract(1991) PDF(507)

Abstract:
In order to further study free edge effect in composite laminates, a new method is developed. This method is based on the perturbation and modified method of least square. In this paper, we emphatically discuss the solution within the boundary layer region, the so-called inner solution. As an example, we will discuss structures composed of two and four symmetric laminates.

Torsion of Rigid Circular Shaft of Varying Diameter Embedded in an Elastic Half Space

Yun Tian-quan

1988, 9(5): 411-415.

Abstract(1805) PDF(358)

Abstract:
The axially symmetric torsion of rigid circular shaft of varying diameter embedded in an elastic half space is studied by line-loaded integral equation method (LLJEM), where the problem is formulated by distributions of ficitious fundamental loads PRCHS (point ring couple in half space) along the axis of symmetry in interval of the shaft and is reduced to a one-dimensional and non-singular Fredholm integral equation of the first kind and is easily solved numerically. Numerical examples oftorsin of rigid conic, cylinder, conical-cylinder embedded in an elastic half space are given and compared with the known result obtained, by the others. The exact solution of torsion of rigid half sphere embedded in an elastic half space is also presented.

The Exact Solution for the General Bending Problems of Conical Shells on the Elastic Foundation

Sun Bo-hua, Huang Yi

1988, 9(5): 417-430.

Abstract(1690) PDF(577)

Abstract:
The general bending problem of conical shells on the elastic foundation (Winkler Medium) is not solved. In this paper, the displacement solution method for this problem is presented. From the governing differential equations in displacement form of conical shell and by introducing a displacement function U(s,θ), the differential equations are changed into an eight-order soluble partial differential equation about the displacement function U(s,θ) in which the coefficients are variable. At the same time, the expressions of the displacement and internal force components of the shell are also given by the displacement function U(s θ). As special cases of this paper, the displacement function introduced by V.S. Vlasov in circular cylindrical shell^[5], the basic equation of the cylindrical shell on the elastic foundation and that of the circular plates on the elastic foundation are directly derived.Under the arbitrary loads and boundary conditions, the general bending problem of the conical shell on the elastic foundation is reduced to find the displacement function U(s,θ).The general solution of the eight-order differential equation is obtained in series form. For the symmetric bending deformation of the conical shell on the elastic foundation, which has been widely usedinpractice,the detailed numerical results and boundary influence coefficients for edge loads have been obtained. These results have important meaning in analysis of conical shell combination construction on the elastic foundation,and provide a valuable judgement for the numerical solution accuracy of some of the same type of the existing problem.

A Computer Model of Pulse Wave and Input Impedance in Human Arteries

Liu Zhao-rong, Zhou Yong-sheng

1988, 9(5): 431-444.

Abstract(1805) PDF(556)

Abstract:
To predict the propagation of pressure and flow pulses in arterial system and the variation of vascular input impedance, a branched and tapered tube model is studied through one-dimensional transient flow analysis. Coupling the continuity and momentum equations yields a group of quasilinear hyperbolic partial differential equations which can be solved numerically by using the method of characteristics. Several boundary conditions of the arterial system are also simplified suitably:The propagation of the pulses of the arterial system and the vascular input impedance is calculated on computer by using the dimensions and the physiological data of the arterial system. The results point out that the pressure and flow pulses of the arterial system and the vascular input impedance produced by this theoretical model is consistent quite well with the experimental results published.

The Geometric New Criterion of Polynomial Stability

Wang Xiao-jun

1988, 9(5): 445-449.

Abstract(1514) PDF(588)

Abstract:
In this paper, we apply the coningacy and boundedness of the zeros for a polynomial f_n(z) with real coefficient a_i (i=0,1,2,…,n). A new simple geometric criterion for stability of f_n(z) is given which is very convenient for application.

Sensitivity Analysis of Truss Structures and Its Application to the Fully Stressed Design

X. Tang, Zhang Xiu-juan

1988, 9(5): 451-458.

Abstract(1588) PDF(584)

Abstract:
Based upon the theorems of structural variations this paper derives a set of expressions for calculating partial derivatives of internal forces, stresses and joint displacements with respect to bar areas for truss structures. Compared with the known formulas for finding the gradients of structural behaviours the calculation effort with the proposed expressions in this paper is usually smaller because the additional virtual loadings needed are relatively fewer. It is of practical significance to various optimization methods in which the calculation of gradients of behaviours is widely used. Moreover, applying the derived formulas to the fully stressed design (FSD), we obtain an improved iterative method for FSD. The numerical examples show that the new method considerably reduces the reanalysis number required to converge to an FSD in comparison with the simple stress ratio method.

The Analysis of the Translation-Torsion Coupling Earthquake Responses of Single-Story Eccentric Factory Buildings with Consideration of Roof Whole-Space-Work

Qu Hua, Wang Huan-ding

1988, 9(5): 459-468.

Abstract(1601) PDF(470)

Abstract:
Scholars at home and abroad have done a great deal of work on analysing translation-torsion coupling earthquake responses of single-story eccentric factory buildings,but all of them ignored the deformation of the roof of the building, This paper simplifies the roof system of the building as an elastic shear beam,According to this scheme, general equations of motion of single-story eccentric factory buildings under the action of horizontal and torsional earthquake components have been established and discussed.In this paper, the translation-torsion coupling earthquake responses of some buildings are calculated and analysed by medal analysis procedure with the use of response spectrum without consideration of the earthquake torsional component. The conclusion of the roof is considered,and the results of calculation are more conformable to the actual earthquake dam age.Moreover,this paper presents a simplified method for calculation and points out the conditions in which the deformation of the roof can be neglected.

Solve a Contact Problem by Optimization Method——to Calculate the Stresses for the Softwheel in a Harmonic Gear

Ye Qing-kai

1988, 9(5): 469-474.

Abstract(1586) PDF(454)

Abstract:
It is difficult to solve the contact problem by usual finite element program. In this paper, we express the contact problem as an optimization problem. In this form we do not need to know all boundary condition in advance. We only need to know the constraint conditions. This method is especially good for solving contact problem. Using this method, we calculate the stresses of the softwheel in the harmonic gear given by Shanghai Jiaotong University, and the results are in good agreement with the experimental results.

1988 Vol. 9, No. 5