应用数学和力学

1990 Vol. 11, No. 7

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Equation in Complex Variable of Axisymmetrical Deformation Problems for a General Shell of Revolution

Qian Wei-zhang

1990, 11(7): 565-579.

Abstract(2078) PDF(649)

Abstract:
In this paper,the equation of axisymmetrical deformation problems for a general shell of revolution is derived in one complex variable under the usual Love-Kirchhoff assumption.In the case of circular ring shells,this equation may be simplified into the equation given by F.Tdlke(1938)[3].R.A.Clark(1950)^[4] and V.V.Novozhilov(1951)^[5].When the horizontal radius of the shell of revolution is much larger than the average radius of curvature of meridian curve,this equation in complex variable may be simplified into the equation for slander ring shells.If the ring shell is circular in shape,then this equation can be reduced into the equation in complex variable for slander circular ring shells given by this author(1979)^[6].If the form of elliptic cross-section is near a circle,then the equation of slander ring shell with near-circle ellipitic cross-section may be reduced to the complex variable equation similar in form for circular slander ring shells.

Strain Path Theory of Plastic Constitutive Relation

Zhao Zu-wu

1990, 11(7): 581-590.

Abstract(2076) PDF(716)

Abstract:
Based on Illiushin's two hypotheses,a new plastic constitutive equation of integral type is proposed.The devialoric stress induced by a strain path consists of two parts which vary according to different laws.Comparison of theoretical calculation with recent experiments is satisfactory.The present theory is not an endochronic theory.

Solution of Simultaneous Equations of Cosine Law Arising from Subjectivity Geometry

Yun Tian-quan

1990, 11(7): 591-595.

Abstract(1822) PDF(472)

Abstract:
This paper discusses the solution of a group of two-order six elements rooted algebraic simultaneous equations set up by cosine law arising from the application example of subjectivity geometry^[1].By means of the implicit function theorem,this paper proves that there exists a unique real solution of those equations.Transforming this problem into an unconstrained nonlinear optimization problem,the solution can be found by known methods.A numerical example by descent method is given.

Asymptotic Solution of Singular Perturbation Problems for the Fourth-Order Elliptic Differential Equations

Su Yu-cheng, Liu Guo-qing

1990, 11(7): 597-610.

Abstract(1925) PDF(611)

Abstract:
In this paper we consider the singularly perturbed boundary value problem for the fourth-order elliptic differential equation,establish the energy estimates of the solutionand its derivatives and construct the formal asymptotic solution by Lyuternik-Vishik's method.Finally,by means of the energy estimates we obtain the bound of the remainder of the asymptotic solution.

A Study of the Postbuckling Path of Cylindricaily Curved Panels of Laminated Composite Materials during Loading and Unloading

Dong Wan-lin, Huang Xiao-qing

1990, 11(7): 611-616.

Abstract(1633) PDF(435)

Abstract:
In this paper,Dynamic Relaxation Method is applied to study the postbuckling path of cylindrically curved panels of laminated composite materials during loading and unloading.The phenomenon that loading paths do not coincide with unloading paths has been found.Numerical results are given for cylindrically curved cross-ply panels subjected to uniform uniaxial compression under two types of boundary conditions.The influence of the number of layers,the panels curvature and the initial imperfection on the postbuckling paths is discussed.

Rate Variational Extremum Principles for Finite Elastoplasticity

Gao Yang, E. T. Onat

1990, 11(7): 617-624.

Abstract(1789) PDF(475)

Abstract:
Dual variational extremum principles for rate problems of classical elastoplasticitv at finite deformation are studied in Updated Lagrangian rate forms.It is proved that the convexity of the variational functionals are closely related to a so-called gap function,which plavs an important role in nonlinear variational problems.

The Solution of a Crack Emanating from an Arbitrary Hole by Boundary Collocation Method

Wang Yuan-han, Li Chun-zhi

1990, 11(7): 625-634.

Abstract(2113) PDF(610)

Abstract:
In this paper a group of stress functions has been proposed for the calculation of a crack emanating from a hole with different shape(including circular,elliptical,rectangular,or rhombic hole) by boundary collocation method.The calculation results show that they coincide very well with the existing solutions by other methods for a circular or elliptical hole with a crack in an infinite plate.At the smae time,a series of results for different holes in a finite plate has also been obtained in this paper.The proposed functions and calculation procedure can be used for a plate of a crack emanating from an arbitrary hole.

Application of One-Parameter Groups of Transformation in Mechanics

Xu Xue-zi, Chen Huai-yong

1990, 11(7): 636-642.

Abstract(2094) PDF(942)

Abstract:
In this paper,including some partial differential equations with a number of independent variables,which can he reduced by the infinitesimal form of the group,we obtain the theory of similarity transformation and its application of the second order nonlinear partial differential equations which have two independent variables and two dependent variables in mechanics.

On J-Integrals Near Models Ⅰ, Ⅱ Crack Tips in the Plates of Orthotropic Composite Material

Yang Wei-yang, Zhang Shao-qin

1990, 11(7): 643-651.

Abstract(1697) PDF(621)

Abstract:
In this paper,we prove the independence of the path of the imegrals near model Ⅰ Ⅱ track tips in the plate of the orthotropic composite material.Then we derive the computing formulae of the J-integrals at the cases of and by using a complex variable method and redueing J-imegrals to compley farm The J-integral computational formulae derived this paper have certain reference value for the theoretical researches and the experimental verifications in the plane fracture for composite material.

On Some Problems in Dynamic Computation for Thin-Walled Structures

Cheng Xiang-sheng

1990, 11(7): 653-657.

Abstract(1615) PDF(478)

Abstract:
This article discusses the problems of the dynamic computation for thin-walled structures such as thin plates and thin shells under impact load to find the dynamic factor mainly.In calculation we take into account the effect of the mass of the striking object and the system of thin-walled structures to be struck and transform the distributed mass of thin-walled structures into only one concentrated "equivalent mass" by the method of reduced mass.Accordingly we derive the dynamic factor for the system of thin-walled structures under impact load.