应用数学和力学

1986 Vol. 7, No. 11

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On the Representation of Finite Rotation in Nonlinear Field Theory of Continuum Mechanics

Chen Zhi-da

1986, 7(11): 959-968.

Abstract(2102) PDF(746)

Abstract:
One of the important basic theoretical problems in the development of continuum mechanics is the separation of finite strain and finite rotation at a point in the displacement field. Now it is certain that S-R decomposition theorem provides a rational theoretical solution for this problem. The purpose of this paper is to clarify some misleading basic concepts of finite rotation of deformed body in current literature, and to promote further progress.

Nonsteady Flow of Groundwater in Aquifer System with Viscoelastic Properties

Liu Ci-qun

1986, 7(11): 969-974.

Abstract(1757) PDF(503)

Abstract:
The transient flow behavior of ground-water in aquifer-aquitard system with viscoelastic properties is studied. On the basis of previous works (Hantush, Neuman, Brutsaert, Corapcioglu), the new partial differential-integral equations are derived. The well-known equations (Hantush, Brutsaert) are the special cases of the new equations. The new equations describe the flow of a slightly compressible groundwater in layers with viscoelastic properties.Analytical solutions of the partial differential-integral equations are obtained by using the method of Laplace transform. The viscoelastic properties enhance the heterogeneities of elastic aquifer system which have delay and feed qualities. The agreements between the numericl inversion results of Laplace transform and the analytical solutions are good. The formulae predict the transient flow behavior of groundwater in this heterogeneous layers.

On the Probabilistic Inner Product Spaces

Zhang Shi-sheng

1986, 7(11): 975-981.

Abstract(2247) PDF(775)

Abstract:
In this paper a new definition for probabilistic inner product spaces is given. By virtue of this definition, some convergence theorems, Schwarz inequality and the orthogonal concept for probabilistic inner product spaces are established and introduced. Moreover, the relationship between this kind of spaces and probabilistic normed spaces is considered also.

Symmetric Formulation of Tangential Stiffnesses for Non-Associated Plasticity

Xiong Wen-lin

1986, 7(11): 983-991.

Abstract(1881) PDF(631)

Abstract:
A numerical scheme is presented which makes it possible to use the symmetric equation solvers in tangential stiffness programs for non-associated materials.

Uniform Convergence for the Difference Scheme in the Conservation Form of Ordinary Differential Equation with a Small Parameter

Ling Peng-cheng

1986, 7(11): 993-1002.

Abstract(1811) PDF(510)

Abstract:
In this paper, we consider a singular perturbation boundary problem for a self-adjoint ordinary differential equaiton. We construct a class of difference schemes with fitted factors, and give the sufficient conditions under which the solution of difference scheme converges uniformly to the solution of differential equation. From this we propose several specific schemes under weaker conditions, and give much higher order of uniform convergence.

Nonlinear Bendings of Unsymmetrically Layered Anisotropic Rectangular Plates

Zhou Ci-qing

1986, 7(11): 1003-1020.

Abstract(1575) PDF(601)

Abstract:
An analysis for the nonlinear bendings of unsymmetrically layered anisotropic rectangular plates subjected to combined edge tensions and lateral loading under venous supports is presented. The uniformly valid N-order asymptotic solutions of the transverse deflection and stress function are derived by the singular perturbation method offered in [1]. The present investigation may provide a simple and convenient method for such a complex problem.

The Generalized Variational Principles about Blending Energy Form of Non-Linear Elasticity

Hu Cheng-dong

1986, 7(11): 1021-1031.

Abstract(1759) PDF(571)

Abstract:
First of all, this paper gives Legendre transformation for the so-called partial corresponding variables of strain energy function Σ(E_ij) and complementary strain energy function ∑^C(S_ij) of the elastic materiel, and introduces the corresponding blending complementary strain energy function ∑_kl^C and blending strain energy function Σ_kl. Moreover, a series of generalized variational principles of the corresponding blending energy form of non-linear elasticity is given. As a special case, there exist corresponding results[1] in linear elasticity.

Dynamical Calculation and Analysis on Penetration of Target Plates by Truncated Conical Projectiles

Gao Shi-qiao, Wang Bao-xing

1986, 7(11): 1033-1038.

Abstract(1846) PDF(481)

Abstract:
In this paper, dynamical calculation and analysis are made on penetration of thin plates by truncated conical projectiles in terms of the needs of fuze designing. The impact velocity ranges from 200w/s ts to 1000m/s (including both low and high velocities). The target plates include the thin aluminium plate (metal) and the plywood (non-metal).Because a strength effect of target plates is considered in the establishment of dynamical models, we solved the problem that some previous models were not suitable to lowvelocity impact, for example, M. Zaid and B. Paul's models.^[1][2][3] Bv comparison of menial effect with strength effect, we theoretically proved Zaid and Paul's experimental conclusion^[3]: "Only when the impact velocity is more that 500m/s can the strength effect be neglected. Otherwise this effect can not be neglected.

Theory of Pressure Swirl Atomisation and Study on the Characteristic of Droplet Size in Atomisation

Lu Ding-yuan

1986, 7(11): 1039-1050.

Abstract(1973) PDF(601)

Abstract:
Based on the observation of the working condition in pressure swirl atomisation experiments, this article tries to suggest a model of the mechanism of pressure swirl atomisation-the atomisation theory of pressure swirl spray of conical film. Under some basic assumptions, the formula for the characteristic of droplet size of pressure swirl atomisation is derived:

The above theory agrees basically with the actual working conditions in atomisation, and gives the latter a compratively good interpretation.In this article, theoretical calculations are worked out for the characteristic of atomised droplet size of some Oil atomising nozzles used in power plants in our country (the People's Republic of China) and are compared with actual test data. The results show that the theory is of some value to preactice, and it is recommended to those concerned for reference.

Elastic-Plastic Fields near Crack Tip Growing Step-by-Step in a Perfectly Plastic Solid

Wang Tzu-chiang

1986, 7(11): 1051-1060.

Abstract(1722) PDF(583)

Abstract:
In this paper, based on the three-dimensional flow theory of plasticity, the fundametal equations for plane strain problem ofelastic-perfectly plastic solids are presented. By using these equations the elastic-plastic fields near the crack tip growing step-by-step in an elastic incompressible-perfectly plastic solid are analysed.The first order asymptotic solutions for the stress field and velocity fields near the crack tip are obtained. The solutions show the evolution process of elastic unloading domain and the development process of central fan domain and reveal the possibility of the presence of the secondary plastic domain. The second order asymptotic solution for stress field is also presented.