应用数学和力学

1990 Vol. 11, No. 10

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Nonlinear Stellar Response to the Growing Spiral Gravitational Disturbance and Its Stabilizing Effect on the Growing Mode

Zhang Bin, Yue Zeng-yuan

1990, 11(10): 843-854.

Abstract(2031) PDF(599)

Abstract:
The nonlinear stellar response to the growing spiral gravitational disturbance is calculated. The result shows that this nonlinear response leads to the increase of Q, and the decrease of the growth rate. This self-regulation mechanism is an important reason for the growing spiral mode to reach a quasi-stationary state eventually.

Substructure Computational Algorithm for Exact Analytic Method

Ji Zhen-yi, Ye Kai-yuan

1990, 11(10): 855-860.

Abstract(2331) PDF(568)

Abstract:
In[1], the exact analytic method for the solution of differential equation with variable coefficients was suggested and an analytic expression of solution was given by initial parameter algorithm. But to some problems such as the bending, free vibration and buckling of nonhomogeneous long cylinders, it is difficult to obtain their solutions by the initial parameter algorithm on computer. In this paper, the substructure computational algorithm for the exact analytic method is presented through the bending of non-homogeneous long cylindrical shell. This substructure algorithm can he applied to solve the problems which can not he calculated by the initial parameter algorithm on computer. Finally, the problems can he reduced to solving a low order system of algehraic equations like the initial parameter algorithm Numerical examples are given and compared with the initial para-algorithm at the end of the paper, which confirms the correctness of the substructure computational algorithm.

Plane Problems of a Finite Disc Containing an Internal Crack

Yin Chang-yan, Zu Cheng-de

1990, 11(10): 861-870.

Abstract(2284) PDF(593)

Abstract:
Using complex variable methods in elasticity, this paper deals with the plane problems ot a finite disc containing an internal linear crack at any position under general loads, obtains the general forms of Complex stress functions and stress-intensity tactors expressed in terms of series, and to these problems disiusses three sposial cases,i.e.the cases of the crack under a uniform pressure, a uniform shear stress and the use of the dise rotating uniformly. In these cases the approximate formulas calcidating the stress-intensity factors are also presented. The calculated results shun that for the middle and.small orachs situated inside the disc and not near the external boundary,these approximate formulas give good or better approximation.

Elasto-Plastic Analysis for the Buckling and Postbuckling of Rectangular Plates under Uniaxial Compression

Shen Hui-shen

1990, 11(10): 871-879.

Abstract(1957) PDF(786)

Abstract:
Full-range analysis for the buckling and post buck ling at rectangular plates under in-plane compression has been made by perturbation technique which takes deflection as its perturbation parameter.In this paper the effects of initial geometric imperfection on the postbuc kling behavior of plates have been discussed. It is seen that the effect of initial imperfection on the inelastic postbuckling oj plates is sensitive. By comparison, it is found that the theoretical results of this paper are in good agreement with experiments.

A Priori Estimate for Maximum Modulus of Generalized Solutions of Quasi-Linear Elliptic Equations

Liang Xi-ting, Wang Xiang-dong

1990, 11(10): 881-892.

Abstract(2576) PDF(618)

Abstract:
Let G he a hounded domain in E Consider the following quasi-linear elliptic equation Although the houndedness of generalized solutions of the equation is proved for very general structural conditions, it does not supply a priori estimate for maximum modulus of solutions. In this paper an estimate to the maximum modulus is made firstly for a special case of quasi-linear elliptic equations, i.e. the and B satisfy the following structural conditions:

Problems of Collinear Cracks between Bonded Dissimilar Materials under Antiplane Concentrated Forces

Liu You-wen, Jiang Chi-ping

1990, 11(10): 893-902.

Abstract(2605) PDF(633)

Abstract:
In this paper problems of collinear cracks between bonded dissimilar materials under antiplane concentrated forces are dealt with. General solutions of the problems are formulated by applying extended Schwarz principle integrated with the analysis of the singularity of complex stress functions. Closed-form solutions of several typical problems are obtained and the stress intensity factors are given. These solutions include a series of original results and some results of previous researches. It is found that under symmetrical loads the solutions for the dissimilar materials are the same as those for the homogeneous materia^[7].

On the Uniqueness of Boundary Integral Equation for the Exterior Helmholtz Problem

Wang Qing, Xu Bo-hou

1990, 11(10): 903-909.

Abstract(2139) PDF(651)

Abstract:
From the point of view of energy analysis, the cause that the uniqueness of the boundary integral equation induced from the exterior Helmholtz problem does not hold is investigated in this paper. It is proved that the Sommerfeld's condition at the infinity is changed so that it is suitable not only for the radiative wave but also for the absorptive wave when we use the boundary integral equation to describe the exterior Helmholtz problem. There fore, the total energy of the system is conservative. The mathematical dealings to guarantee the uniqueness are discussed based upon this explanation.

Gibbs-Appells Equations of Variable Mass Nonlinear Nonholonomic Mechanical Systems

Qiao Yong-fen

1990, 11(10): 911-920.

Abstract(2253) PDF(722)

Abstract:
In this paper, the Gibbs-Appell's equations of motion are extended to the most general variable mass nonholonomie mechanical systems. Then the Gibbs-Appell's equations of motion in terms of generalized coordinates or quasi-coordinates and an integral variational principle of variable mass nonlinear nonholonomie mechanical systems are obtained. Finally, an example is given.

The Constitutive Equation Resemblance of Elastic-Plastic Multiphase Solid

Zhang Pei-yuan, Tang Yu

1990, 11(10): 921-930.

Abstract(2212) PDF(583)

Abstract:
Based on composite materials, the equivalent elastic-plastic constitutive equations of multiphase solid are researched. According to the suggested definition of. constitutive equivalence it is demonstrated that the multiphase solid, composed of several kinds of homogeneous elastic-plastic media that conform to the generalized normality rule, has the same type of constitutive equations as its constituents have that also conform to the generalized normality rule.

A Precise Singular Finite Element for Crack Analysis

Wang Yan-qun, Zhang Jing-yu

1990, 11(10): 931-936.

Abstract(2135) PDF(602)

Abstract:
The multi-variable finite element algorithm based on the generalized Gulerkin's method is more flexible to establish a finite element model in the continuum mechanics. By using this algorithm and numerical tests a new singular finite element for elasto-plastic fracture analysis has been formulated. The results of numerical tests show that the new element possesses high accuracy and good performance. Some rules for formulating a multi-variable singular finite element are also discussed in this paper.