应用数学和力学

1998 Vol. 19, No. 5

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On the Stress Concentration in Thick Cylindrical Shells with an Arbitrary Cutout

Hu Chao, Liu Diankui, Ma Xingrui, Wang Benli

1998, 19(5): 373-384.

Abstract(2424) PDF(716)

Abstract:
In this paper,based on the theory of thick shells including effects of transverse shear deformations,a complex variable analytic method to solve stress concentrations in circular cylindrical shells with a small cutout is established.A general solution and expression satisfying the boundary conditions on the edge of arbitrary cutouts are obtained.The stress problem can be reduced to the solution of an infinite algebraic equation series,and can be normalized by means of this method.Numerical results for stress concentration factors of the shell with a small circular and elliptic cutout are presented.

Postbuckling of Imperfect Stiffened Cylindrical Shells under Combined External Pressure and Heating

Shen Huishen

1998, 19(5): 385-398.

Abstract(2441) PDF(574)

Abstract:
A postbuckling analysis is presented for a stiffened cylindrical shell of finite length subjected to combined loading of external pressure and a uniform temperature rise.The formulations are based on a boundary layer theory of shell buckling,which includes the effects of nonlinear prebuckling deformations,nonlinear large deflections in the postbuckling range and initial geometrical imperfections of the shell.The "smeared stiffener" approach is adopted for the stiffeners.The analysis uses a singular perturbation technique to determine the interactive buckling loads and the postbuckling equilibrium paths.Numerical examples cover the performances of perfect and imperfect,stringer and ring stiffened cylindrical shells.Typical results are presented in dimensionless graphical form.

Some Exact Results Concerning Thermoelastic Properties of Hollow Sphere Composites

He Linghui, Cheng Zhenqiang, Liu Renhuai

1998, 19(5): 399-406.

Abstract(1941) PDF(762)

Abstract:
Thermoelastic properties of hollow sphere composites are studied,based on the uniform matrix-field concept proposed here.Some connections between local thermal and mechanical fields produced by certain homogeneous boundary conditions are derived,and furthermore,exact relations are also obtained between the effective thermoelastic properties of the composites.For a macroscopically isotropic composite with a certain ratio of the outer radius to the inner radius,it is found that the effective bulk modulus and the linear coefficient of thermal expansion can be exactly determined,if the thermal expansion coefficient of the matrix and that of the sphere are the same.

The General Stress Strain Relation of Soils Involving the Rotation of Principal Stress Axes

Liu Yuanxue, Zheng Yingren, Chen Zhenghan

1998, 19(5): 407-413.

Abstract(2409) PDF(1176)

Abstract:
In the light of matrix theory,the character of stress increment which causes the rotation of principal stress axes is analysed and the general stress increment is decomposed into two parts:coaxial part and rotational part.Based on these,the complex three dimension(3-D)problem involving the rotation of principal stress axes is simplified to the combination of the 3-D coaxial model and the theory about pure rotation of principal stress axes that is only around one principal stress axes.The difficulty of analysis is reduced significantly.The concrete calculating method of general 3-D problems is provided and other applications are also presented.

The Approximate Analytical Solution for the Buckling Loads of a Thin-Walled Box Column with Variable Cross-section

Xie Yongjiu, Ning Qinghai, Chen Minglun

1998, 19(5): 415-424.

Abstract(2202) PDF(642)

Abstract:
For a thin-walled box column with variable cross-section,the three governing equations for torsional-flexural buckling are ordinary differential equations of the second or fourth order with variable coefficients,so it is very difficult to solve them by means of an analytic method.In this paper,Polynomials are used to approximate the geometric properties of cross-section and certain coefficients of the differential equations.Based on the energy principle and the Galerkinc's method,the approximate formulas for calculating the flexural and torsional buckling loads of this kind of columns are developed respectively,and numerical examples are used to verify the correctness of the solutions obtained. The results calculated in this paper provide the basis for demonstrating the stability of thin-walled box columns with variable cross-section.This paper is of practical value.

The Stability in Neural Networks with Interneuronal Transmission Delays

Cao Jinde, Li Jibin

1998, 19(5): 425-430.

Abstract(2420) PDF(703)

Abstract:
In this paper,some sufficient conditions are obtained for the global asymptotic stability of the equilibrium of neural networks with inter neuronal transmission delays of the type

A Crack Emanating from the Tip of Bonded Dissimilar Materials

Qian Jun, Norio Hasebe

1998, 19(5): 431-445.

Abstract(2277) PDF(485)

Abstract:
A crack is assumed to emanate from the tip of bonded dissimilar materials with the crack on the bisector of one of the bonded wedges.The problem is firstly divided into symmetric and anti-symmetric modes according to the characteristics of the local geometry.By eigenexpansion method,the eigenequations for the two modes are derived,respectively,and the corresponding eigenvalues are obtained with different ratios of dissimilar material constants and angles of the wedges.The singularity of the crack is then analyzed by the eigenvalues that are less then one.The fields of displacement and stress in the vicinity of the tip of the crack are finally derived in an explicit form.

Integration Method for the Dynamics Equation of Relative Motion of Variable Mass Nonlinear Nonholonomic System

Chen Xiangwei, Luo Shaokai

1998, 19(5): 447-455.

Abstract(2490) PDF(797)

Abstract:
In this paper,the integration methods of dynamics equations of relative motion of variable mass nonlinear nonholonomic system,such as the gradient method,the single-component method and the field method,are given.Firstly,the dynamics equations are written in the canonical form and the field form.Secondly,the gradient method,the single-component method and the field method are used to integrate the dynamics equations of the corresponding constant mass holonomic system in inertial reference frame respectively.With the restriction of nonholonomic constraints to the initial conditions being considered,the solutions of the dynamics equations of variable mass nonlinear nonholonmic system in noninertial reference frame are obtained.

The Semi-Discrete Method for Solving High-Dimension Wave Equation

Wu Jiancheng, Cai Rizeng

1998, 19(5): 457-464.

Abstract(2549) PDF(559)

Abstract:
The article gives a semi-discrete method for solving high-dimension wave equation.By using the method,high-dimension wave equation is converted by means of discretization into 1-D wave equation system which is well-posed.The convergence of the semi-discrete method is given.The numerical calculating results show that the speed of convergence is high.

A New High-Order Accuracy Explicit Difference Scheme for Solving Three-Dimensional Parabolic Equations

Ma Mingshu

1998, 19(5): 465-469.

Abstract(2372) PDF(825)

Abstract:
In this paper,a new three-level explicit difference scheme with high accuracy is proposed for solving three-dimensional parabolic equations.It is shown that the truncation error of the scheme is O(Δt²+Δx⁴)and the condition of stability of the scheme is r≤1/4.