应用数学和力学

1992 Vol. 13, No. 8

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An Exact Element Method for Bending of Nonhomogeneous Thin Plates

Ji Zhen-yi, Yeh Kai-yuan

1992, 13(8): 659-666.

Abstract(1963) PDF(537)

Abstract:
In this paper, based on the step reduction method, a new method, the exact element method for constructing finite element, is presented. Since the new method doesn't need the variational principle, it can be applied to solve non-positive and positive definite partial differential equations with arbitrary variable coefficient. By this method, a triangle noncompatible element with 6 degrees of freedom is derived to solve the bending of nonhomogeneous plate. The convergence of displacements and stress resultants which have satisfactory numerical precision is proved. Numerical examples are given at the end of this paper, which indicate satisfactory results of stress resultants and displacements can be obtained by the present method.

Generalized Complementarity Problems for Fuzzy Mappings

Zhang Shi-sheng, Huang Nan-jing

1992, 13(8): 667-675.

Abstract(1689) PDF(569)

Abstract:
In this paper we introduce a new class of generalized complementarity problems for the fuzzy mappings and construct a new iterative algorithm. We also discuss the existence of solutions for the generalized complementarity problems and the convergence of iterative sequence.

Spectral-Finite Element Method for Compressible Fluid Flow

Guo Ben-yu, Cao Wei-ming

1992, 13(8): 677-692.

Abstract(1897) PDF(634)

Abstract:
In this paper, a combined Fourier spectral-finite element method is proposed for solving n-dimensional (n=2,3), semi-periodic compressible fluid flow problems. The strict error estimation as well as the convergence rate, is presented.

Elapsed Time of Periodic Motion with Negative Damping

Li Yi-ping

1992, 13(8): 693-697.

Abstract(2071) PDF(553)

Abstract:
An initially periodic motion is gradually raised out of the potential well by the effect of negative damping. The elapsed time when the motion ceases to be periodic is obtained by multiple variable expansions. An example of a strictly nonlinear system shows the result has a good approximation and is easy to calculate.

The Existence of Buckled States on a Perforated Thin Plate

Cheng Chang-jun, Yang Xiao

1992, 13(8): 699-709.

Abstract(1826) PDF(603)

Abstract:
On the basis of the generalized von Kármán theory for perforated thin plates established in [1,2], the existence of buckled states for perforated plates subjected to self-equilibrating inplane forces along each edge systematically is investigated. This work completely generalizes the results in [3, 4].

An Effective Boundary Method for the Analysis of Elastoplastic Problems

Hu Ning

1992, 13(8): 711-718.

Abstract(1976) PDF(426)

Abstract:
In this paper, a series of effective formulae of the boundary element method is presented. In these formulae, by using a new variable, two kernels are only of the weaker singularity of Lnr (where r is the distance between a source point and a field point). Hence, the singularities in the conventional displacement formulation and stress formulation at internal points are reduced respectively so that the "boundary-layer" effect which strongly degenerates the accuracy of stress calculation by using original formulae is eliminated. Also the direct evaluation of coefficients C (boundary tensor), which are difficult to calculate, is avoided. This method is used in elastoplastic analysis. The results of the numerical investigation demonstrate the potential advantages of this method.

The Estimation of Solution of the Boundary Value Problem of the Systems for Quasi-Linear Ordinary Differential Equations

Huang Wei-zhang

1992, 13(8): 719-727.

Abstract(2307) PDF(635)

Abstract:
This paper deals with the singular perturbation of the boundary value problem of the systems for quasi-linear ordinary differential equations x'=f(t,x,y,ε),x(0,ε)=A(ε) εy"=g(t,x,y,ε)y'+h(t,x,y,ε) y(0,ε)=B(ε),y(1,ε)=C(ε) where x,f, y, h, A, B and C all belong to Rⁿ, and g is an n×n matrix function. Under suitable conditions we prove the existence of the solutions by diagonalization and the fixed point theorem and also estimate the remainder.

A Microscopic Damage Model Considering the Change of Void Shape and Application in the Void Closing

Zhu Ming, Jin Quan-lin

1992, 13(8): 729-736.

Abstract(1792) PDF(430)

Abstract:
A microscopic damage model of ellipsoidal body containing ellipsoidal void for nonlinear matrix materials is developed under a particular coordinate. The change of void shape is considered in this model. The viscous restrained equation obtained from the model is affected by stress ∑_ij, void volume fraction f, material strain rate exponent m as well as the void shape. Gurson's equation is modified from the numerical solution. The modified equation is suitable for the case of nonlinear matrix materials and changeable voids. Lastly, the model is used to analyze the closing process of voids.

The Analogue Simulation Criterion of the Cavitation

Huang Jing-quan

1992, 13(8): 737-740.

Abstract(2184) PDF(692)

Abstract:
Employing the available theory, the analogue simulation criterion of the cavitation is introduced to provide the basis for the analogue simulation of the cavitation.

Hydrostatic Stress-Dependent Perfectly-Plastic Stress Fields at a Stationary Plane-Stress Crack-Tip

Lin Bai-song

1992, 13(8): 741-744.

Abstract(2500) PDF(504)

Abstract:
Under the condition that all the stress components at a crack-tip are the functions of θ only, making use of equilibrium equations and hydrostatic stress-dependent yield condition, in this paper, we derive the generally analytical expressions of the hydrostatic stress-dependent perfectly-plastic stress fields at a stationary plane-stress crack-tip. Applying these generally analytical expressions to the concrete cracks, the analytical expressions of hydrostatic stress-dependent perfectly-plastic stress fields at the tips of mode Ⅰ and mode Ⅱ cracks are obtained.

Nonlinear Vibration and Thermal-Buckling of a Heated Annular Plate with a Rigid Mass

Li Shi-rong

1992, 13(8): 745-751.

Abstract(2227) PDF(616)

Abstract:
On the basis of Hamilton's principle and dynamic version of von Kármán's equations, the nonlinear vibration and thermal-buckling of a uniformly heated isotropic annular plate with a completely clamped outer edge and a fixed rigid mass along the inner edge are studied. By parametric perturbation and numerical differentiation, the nonlinear response of the plate-mass system and the critical temperature in the mid-plane at which the plate is in buckled state are obtained. Some meaningful characteristic curves and data tables are given.