应用数学和力学

1991 Vol. 12, No. 12

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A Weighted Residual Method for Elastic-Plastic Analysis near a Crack Tip and the Calculation of the Plastic Stress Intensity Factors

Zhang Ning-sheng, Zhao Xue-ren, Hsueh Dah-wei

1991, 12(12): 1055-1066.

Abstract(2867) PDF(530)

Abstract:
In this paper, a weighted residual method for the elastic-plastic analysis near a crack tip is systematically given by taking the model of power-law hardening under plane strain condition as a sample. The elastic-plastic solutions of the crack lip field and an approach based on the superposition of the nonlinear finite element method on the complete solution in the whole crack body field, to calculate the plastic stress intensity factors, are also developed. Therefore, a complete analvsis based on the calculation both for the crack tip field and for the whole crack body field is provided.

Coexistence of the Chaos and the Periodic Solutions in Planar Fluid Flows

Yuan Xiao-feng, Guo Rui-hai

1991, 12(12): 1067-1074.

Abstract(2286) PDF(462)

Abstract:
This paper discusses the dynamic behavior of the Kelvin-Stuart cat's eye flow under periodic perturbations. By means of the Melnikov method the conditions to have bifurcations to subharmonics of even order for the oscillating orbits and to have bifurcations to subharmonics of any order for the rotating orbits are given, and further, the coexistence phenomena of the chaotic motions and periodic solutions are presented.

Application of the Modified iteration Method to Nonlinear Postbuckling Analysis of Thin Circular Plates

Li Dong

1991, 12(12): 1075-1080.

Abstract(2254) PDF(442)

Abstract:
In this paper, the modified iteration method is further generalized to the study of axisymmetrical postbuckling of thin circular plates and hereby a new approximate analytic solution of the problem is obtained. Further utilizations of this method to postbuckling analyses of plates of more complicated structure are expected.

A Group of Chaotic Motion of Soft Spring Quadratic Duffing Equations

Cheng Fu-de

1991, 12(12): 1081-1085.

Abstract(2699) PDF(456)

Abstract:
In this paper, we use the Melnikov function method to study a kind of soft Duffing equations^[1] (k=1,2,3…) and give the condition that the equations have chaotic motion and bifurcation. The method used in this paper is effective for dealing with the Melnikov function integral of the system whose explict expression of the homoclinic or heteroclinic orbit cannot be given.

Stability of Laminated Composite Circular Conical Shells under External Pressure

Wang Hu, Wang Tsun-kuei

1991, 12(12): 1087-1095.

Abstract(2603) PDF(523)

Abstract:
In this paper, based on the mixed-type theory developed by the same authors^[1], a theoretical analysis is presented for the stability of laminated composite circular conical shells under external pressure. The formulas for critical external pressure are obtained by using the potential energy variation principle. Very good agreement is shown between the theoretical prediction of critical external pressure and the experimental data. Finally, the influence of some parameters on critical external pressure is discussed numerically. The mixed-type theory developed by the same authors[1] and the results obtained in this paper are very useful in aerospace engineering design.

A Tensor Method for the Derivation of the Equations of Rigid Body Dynamics

Tao Qing-sheng

1991, 12(12): 1097-1102.

Abstract(3236) PDF(494)

Abstract:
A tensor method for the derivation of the equations of rigid body dynamics, based on the concepts of continuum mechanics, is presented. The formula of time derivative of the inertia tensor with zero corotational rate is used to prove the equivalences of five methods, namely, Lagrange's equations, Nielsen's equations, Gibbs-Appell's equations, Kane's equations and the generalized momentum type of Kane's equations. Some differential identities on angular velocity and angular acceleration are given.

On Vibration of Hemispherical Shell by Using Finite Element Method

Fan Shang-chun, Liu Guang-yu, Wang Zhen-jun

1991, 12(12): 1103-1109.

Abstract(2109) PDF(587)

Abstract:
This paper establishes the finite element equation for the spherical shell. The resonant frequencies of the above shell under different boundary conditions are also discussed and calculated.

On the Properties of Elastic-Viscous Fluid Flow past an Obstacle

Ma Dan-lin, Huang Kuan-yuan

1991, 12(12): 1111-1119.

Abstract(2203) PDF(507)

Abstract:
Fundamental equations for the analysis of plane flow of elastic-viscous fluid are established. On such a basis, a perturbed-weighted residual finite element model for small Deborah number situations is formulated. The model is further incorporated for investigations on the behavioral characteristics of the elastic-viscous fluid flow when passing an obstacle, which include the mechanisms of the retardation of separation point, and the reduction of drag forces and so forth. The numerical investigations demonstrate the favorable advantages of the present model in its remarkable simplicity and reasonable accuracy attained in plane flow analysis.

The Automatic Generation of Limit State Function of Hinged Structure

Che Wei-yi

1991, 12(12): 1121-1126.

Abstract(2111) PDF(635)

Abstract:
In this paper, the theorem of structure continual variation of truss structure in the analysis of structure reliability is derived, and it is used to generate limit state function automatically. We can avoid repeated assembly of global stiffness matrix and repeated inverse operations of the matrix caused by constant changes of structure topology. A new criterion of degenerate of the structure into mechanism is introduced. The calculation examples are satisfactory.

Buckling and Postbuckling of Stiffened Cylindrical Shells under Axial Compression

Shen Hui-shen, Zhou Pin, Chen Tie-yun

1991, 12(12): 1127-1139.

Abstract(2631) PDF(491)

Abstract:
Buckling and postbuckling behaviors of perfect and imperfect, stringer and ortho/ropically stiffened cylindrical shells have been studied under axial compression. Based on the boundary la ver theory for the buckling of thin elastic shells suggested in ref. [1], a theoretical analysis is presented. The effects of material properties of stiffenefs and skin, which are made of different materials, on the huckling load and postbuckling behavior of stiffened cylindrical shells have also been discussed.

The Stability of Difference Schemes of a Higher Dimensional Parabolic Equation

Sun Qi-ren

1991, 12(12): 1141-1147.

Abstract(2134) PDF(502)

Abstract:
This paper proposes a new method to improve the stability condition of difference scheme of a parabolic equation. Necessary and sufficient conditions of the stability of this new method are given and proved. Some numerical examples show that this method has some calculation advantages.

The Boundary Expanding-Contracting Principle

Song Shun-cheng

1991, 12(12): 1149-1152.

Abstract(2074) PDF(447)

Abstract:
In paper [5], we proposed the boundary expanding-contracting principle and the boundary expanding-contracting method(BECM). In this paper we make some complemental statements and detailed proofs about the principle.