应用数学和力学

1994 Vol. 15, No. 2

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Three Dimensional Stress Analysis of Symmetric Composite Laminates under Uniaxial Extension and in-Plane Pure Shear

Chien Wei-zang, Huang Qian, Feng Wei

1994, 15(2): 95-103.

Abstract(2248) PDF(584)

Abstract:
This paper presents the stress and strain distribution obtained numerically in the thickness direction in the central region of symmetric composite laminatesunder uniaxial exlension and in-plane pure shear loading. It is shown that in the symmetric angleply laminates,near the interlaminar surface,there is an interlaminar boundary-layer effect.The abrupt change of the fiber orientation at the interlaminar surface causes a high concentration of stresses and a local three dimensional stress state.

The Temperature Analysis of the Billet with Phase Change during Continuous Casting

Zhao Xing-hua, Cheng Xiao-di

1994, 15(2): 105-113.

Abstract(2122) PDF(515)

Abstract:
In this paper,the problem of 3-D steady heat conduction including the influence of phase change on billets is turned into the 2-D transient problem by a suitable transformation technique. The effective specific heat has been employed to substitute for the effect of the phase ceange.The computational formulation of finite element has been presented. And the careful disposal of the phase change region has also been given.

Iterative Process for Lipschitz Local Strictly Pseudocontractive Mappings

Deng Lei, Ding Xie-ping

1994, 15(2): 115-119.

Abstract(2114) PDF(509)

Abstract:
Suppose that K is a non-empty subset of uniformly smooth Banach space X.Let T:K→X be a Lipschitz local strcily pseudocontractine mapping.In this paper,the iterative sequence which converges strongly to the unique fixed point of Tis given.A related result deals with the problem that the Ishikawa iteration process canverges strongly to a solution of the equation TX-f when T is Lipschitzian and local strongly accretive in X.

A Rate Type Method for Large Deformation Problems of Nonllnear Elasticity

Liang Fei, Zhang Shan-yuan

1994, 15(2): 121-128.

Abstract(1854) PDF(580)

Abstract:
In this paper, we obtain the rate-tvpe constitutive expressions of the nonlinear isotropic elastieity by using the Jaumann, Truesdell and Green-Naghdi stress rate respectively,Through analysing the simple shear deformation for Mooney-Rivlin material,three kinds of rate-type constitutive equations are verified to be equivalent to the original equation.Rate-type variational prineiples are also presented, and the Ritzmethod is used to obtain the numerical solution of a reetangular rubber membrane under uniaxial stretch.

On the Solution of Two Co-Affected Spedies

Zhang Wei-fu, Lü Rong-qing

1994, 15(2): 129-138.

Abstract(2103) PDF(450)

Abstract:
This paper discusses a model of two coeffected species with diffusion system,where the birth functions have the characteristic index decline, and then the eircumstance factors α_i which are connected with natural resources, and the birth parameters β_i which could be controlled are introduced.By means of the upper-lowersolutions,the existence,uniqueness and the local stability of equilibrium solution of the moel are discussed.It's discovered that the birth parameters β_i determine the developing tendency when other parameters are comparatively stable.

First lntegrals and lntegral lnvariants for Variable Mass Nonholonomic System in Noninertial Reference Frames

Luo Shao-kai

1994, 15(2): 139-146.

Abstract(2355) PDF(514)

Abstract:
The first integrals and their conditions of existence for variable massnonholonomic system in noninertial relerence frames are obtained,and the canonicalequations and the variation equations of the system are extended. It is proved that using the first integral we can construct the integral invariant of the system.Finally,a series of deductions and an example are given.

Longituanal Shear Problems of Collinear Rigid Line Inclusions in Anisotropic Materials

Jiang Chi-ping

1994, 15(2): 147-154.

Abstract(2122) PDF(603)

Abstract:
Longitudinal shear problems of collinear rigid line inclusions (sometimes called hard crack or inverse crack problems) in anisotropic materials are dealt with. By usingthe conplex variable method, we present the formulation of the general problem and the closed form solutions to some problems of practical importance, The atress distribution in the immediate vicinity of the rigid line end is examined. The corresponding formulation and solutions for isotropic materials can be arrived at from the special cases of those in the present paper, some of which are in agreement with the existing results^[1].

Bending Integral Expressions of as Cylinder with Cracks

Wang Xiao-chun

1994, 15(2): 155-157.

Abstract(1564) PDF(514)

Abstract:
In this paper,based on paper [1] and [2], bending integral expressions of the stress function and shear stresses of a cylinder with several cracks are obtained. Using the numerical method of the singular integral equations^[3],it is easy for us to do the numerical calculation of the stresses and stress intensity factors, which is similar to that of paper[1].

Generaliaed Biharmonic Operator and Its Application to the Bending of Elastic Thin Plates

Yu Zhong-zhi

1994, 15(2): 159-165.

Abstract(1871) PDF(443)

Abstract:
In this paper, δ-function is used to construct the generalized biharmonic operators, the corresponding quadratic function is presented, and the latter is applied to the bending of elastic thin plates, The result shows that when the arguments in the variational functional are generalized functions, discontinuity to sone degree is allowed, and the modified variational principle by using the Lagrange multipliers is merely a special form of the result mentioned above.

Centrifugal Inertia Effects of the Fluid Flow between Stepped Spherical Surfaces

Liu Zhen-bei

1994, 15(2): 167-177.

Abstract(1544) PDF(453)

Abstract:
This paper generalizes and applies method of the Sommerfeld transformation,therefore,the analytical solutions of the fluid flow between stepped spherical surfacesare derived when the centrifugal inertial effects are taken into consideration. It presents a theoretical basis for exact design of the spherical hydrostatic thrust bearing.

A New Hybrid Quadrilateral Finite Element for Mindlin Plate

Chin Yi, Zhang Jing-yu

1994, 15(2): 179-188.

Abstract(2307) PDF(493)

Abstract:
In this paper a new quadrilateral plate element concerning the effect of transverse shear strain has been presented. It is derived from the hybrid finite element model based on the principles of virtual work. The outstanding advantage of this element is to use more rational trial functions of the displacements. For this reason, every variety of plate deformation can be simulated really whilc the least degrees of freedom is employed.A wide range of numerical tests was conducted and the results illustrate that this element has a very wide application scope to the thickness of plates and satisfactory accuracy can be obtained by coarse mesh for all kinds of examples.