应用数学和力学

1990 Vol. 11, No. 1

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On Unilateral Contact Large Deformation Problem with Friction——(Ⅱ) Nonlinear Finite Element Technique and Its Application

Shang Yong, Chen Zhi-da

1990, 11(1): 1-11.

Abstract(1976) PDF(776)

Abstract:
Based on the variational equation derived in ref.[1], a nonlinear incremental F.E. equation is formulated for unilateral contact elastic and plastie large deformation problems. A new technique-co-moving coordinate finite element method is introduced, and a practical mathematical model for large deformation contact problem is described. To show the effectiveness of the method, problems of contact large deformation of cantilever bean, circular plate, as well as metal ring are computed. Compared with experiments, the results show good agreements.

Application of the Modified Iteration Method to Nonlinear Vibration of Corrugated Circular Plates

Li Dong, Liu Ren-huai

1990, 11(1): 13-21.

Abstract(1711) PDF(733)

Abstract:
In this paper, the modified iteration method is successfully exended to investigate the nonlinear free vibration of corrugated circular plates with full corrugations. The analytical relation for the amplitude-frequency response of corrugated circular plates is obtained and discussions on the influences of geometrical parameters on vibration behaviours of corrugated circular plates are made. The present results arc practically important in the design of elastic elements in precision instruments.

A New Higher-Order Theory to Laminated Plates and Shells

Zeng Jia-xiong, Fan Ye-li

1990, 11(1): 23-32.

Abstract(1923) PDF(534)

Abstract:
In this paper, a new highcr-ortler theory to luminated plate and shells is presemed and then symmetric and antisymmetric cross-ply laminated plates, cyliadric bending and heading of spherical shells are also studied. In order to examine the accuracy of the theory, several particular examples have been calculated. The numerical results are in good agreement with the exact solution, which shews the theory is possessed of higher accuracy and is easy to solve a problem with few unknowns.

Viscoplastic Field near a Propagating Crack-Tip

Gao Y. C.

1990, 11(1): 33-43.

Abstract(1535) PDF(687)

Abstract:
An clastic-vise oplastic constitutive model is proposed instead of the usual elastoplastic model. It is assumed tha when crack-lip is approached the viscosity coefficient tends to zero (η=η₀r). Asymptoic analysis of the dynamic field near a propagating crack-tip is given, and the uniparameler solution is obtained. The numerical result is given for various Mach number and viscosity coefficient, Based on the asymptotic solution, a fracture criterion is proposed and the stability of crack propagation is discussed.

Some Problems in Boundary Element Programming of Axisymmetric Elasticity

Lü Pin Huang, Mao-kuang

1990, 11(1): 45-52.

Abstract(1706) PDF(446)

Abstract:
Axisyminetric problems in elasticity can be reduced to two dimensional ones, but they are a little more complicated than plane problems. Therefore, some special problems will be encountered in the boundary element programming of axisymmctric elasticity. In this paper, the methods to treat these problems and some remarks are given according to our experience in programming. Numerical examples are presented for the checking of these treatments.

A Note on Derivatives of Function and Their Fourier Transforms in L₂

Zhou Xiao-zhong, Liu Xing-quan

1990, 11(1): 53-60.

Abstract(1834) PDF(509)

Abstract:
The purpose of this article is to indicate the shortcomings of a few theorems of [1]. Moreover, some interesting results are detluced.

Dynamic Buckling Mode of an Elastic Bar

Li Qing-ming

1990, 11(1): 61-66.

Abstract(2170) PDF(723)

Abstract:
The conception of buckling relative initial imperfection is presented in this paper. According to Bernoulli-Euler beam equation, the dynamic buckling mode of an elastic bar under the homogeneous boundary conditions can he derived by applying the preferred mode analytical method. As an example, the dynamic buckling mode of an elastic bar clamped at both ends is discussed.

Completely Exponentially Fitted Finite Difference Methods for Problems of Turning Point

Chen Ming-lun, Wang Guo-ying

1990, 11(1): 67-77.

Abstract(1883) PDF(525)

Abstract:
In this paper we construct a completely exponentially fitted finite difference scheme for the boundary value problem of differential equation with turning points, extending Miller's method^[1] and simplifying the method of the proof. We prove the first order uniform convergence of the scheme. The numerical results show that it is better than Il'in's scheme.

Evolution of Slowly Modulated Wave Train on Porous Sea Bed

Tang Ling, Liu Yin-zhong

1990, 11(1): 79-86.

Abstract(1739) PDF(489)

Abstract:
In this paper, the problem of evolution of slowly modulated wave train on porous sea bed is investigated with the method of multiple scales. For the sea water in the upper region, the classical potential theory is used while the fluid motion in the porous sea bed is described by Darcy's law. The equations of the first and second order modulations of wave amplitude are derived by using matching conditions on the sea bed. The corresponding solutions are found and seepage pressures are also given at the same time.

Existence and Uniqueness of Periodic Solutions for Fourth-Order Nonlinear Periodic Systems

Jin Jun

1990, 11(1): 87-94.

Abstract(1761) PDF(576)

Abstract:
In this paper, we study the existence, uniqueness and stability of the periodic solutions for fourth-order nonlinear nonhomogeneous periodic systems with slowly changing coefficients by using the method of Liapunor Function.We obtain some sufficient conditions which guarantee the existence, uniqueness and asymptotic stability of the periodic solutions of these systems and estimate the extent to which the coefficients are allowed to change.