应用数学和力学

1996 Vol. 17, No. 10

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Quasi-Principal Axis Method in Finite Deformation

Zheng Quanshui

1996, 17(10): 857-868.

Abstract(2025) PDF(568)

Abstract:
A quasi-quasi-principal axis frame means a unit orthogonal frame in which the shear strains are small. As an extension of Hill's principal axis method we establish the approximate representations for various strains, the finite rotation tensor, spins, strain rates, conjugate stresses and their rates with respect to quasi-principal axes. The quasiprincipal axis method may function as a new basis of numerically analyzing finite deformation problems.

Anisotropic Effects of Quasi-Isotropic Composites(Ⅰ)──Modelling

Zheng Quanshui, Fang Huiyu

1996, 17(10): 869-876.

Abstract(2461) PDF(1088)

Abstract:
Experimental obseryations show that quasi-isotropic materials, such as N-axial fibre-reinforced composites and woven materials, exhibit various degrees of anisotrpy in elasticity and strength, and the anisotropy in strengty is normally stronger than that in elasticity.In view of some available experimental data and based on the general formulation of the constitutive equations and failure criteria of quasi-isotropic materials established by using the theory of repesentations for tensor functions, we postulate several applicable models of the constitutive equations and strength for 3 and 4-axial quasi-isotropic materials to reveal the anisotropic effects In a continued work (Part II) the anisotropic effect in strength of an infintely large plate with a single elliptical hole or crack is studied, and the proposed stiffness and strength modelsare verified in terms of micro-mechanical analyses.

Anisotropic Effects of Quasi-Isotropic Composites(Ⅱ)──Applications and Micro-Nlechanical Analysis

Fang Huiyu, Zheng Quanshui

1996, 17(10): 877-882.

Abstract(1896) PDF(474)

Abstract:
Up to now the analysis on aisnotropic effects of quasi-isotropic composites to material structures has not been found in literatures. In the present paper the strength model for triaxial woven materials proposed in Part (I)^[1] is applied to study the problems of an infintiely large plate of triaxial woven material containing either an either an elliptic hole or a crack. To the elliptic hole problem the remote coritical loading as a function of the geometric parameters of woven materials is analysed and to the crack problem, the cracking orientation is examined. Finally the elasticity and strength models for a triaxial woven material proposed in Part (I) are verfied in terms of micromechanical analysis.

On Unilaterally Constrained Motions of Rigid Bodies Systems

Li Hongbo

1996, 17(10): 883-887.

Abstract(1882) PDF(559)

Abstract:
In this paper, the unilaterally constrained motions of a large class of rigid bodies systems are studied both locally and globally. The main conclusion is that locally,such a system bahaves like a particle in a Riemannian manifold with boundary, globally, under the assumption of energy conservation, the system behaves like a billiards system over a Riemannina manifold with boundary.

Principal Axis intrinsic Method and the High Dimensional Tensor Equation AX-XA=C

Liang Haoyun

1996, 17(10): 889-894.

Abstract(2138) PDF(487)

Abstract:
The present paper spreads the principal axis intrinsic method to the high dimensional case and discusses the solution of the tensor equation AX-XA=C.

Contact Problems and Dual Variational Inequality of 2-D Elastoplastic Beam Theory

Gao Yang

1996, 17(10): 895-908.

Abstract(2215) PDF(485)

Abstract:
In order to study the frictional contact problems of the elastoplastic beam theory,an extended two-dimensional beam model is established, and a second order nonlinear equilibrium problem with both internal and external complementarity conditions is proposed. The external complementarity condition provides the free boundary condition. While the internal complemententarity condition gives the interface of the elastic and plastic regions. We prove that this bicomplementarity problem is equivalent to a nonlinear variational inequality The dual variational inequality is also developed.It is shown that the dual variational inequality is much easier than the primalvariational problem. Application to limit analysis is illustrated.

Internal Variables and Thermodynamic Modeling of Pseudoelasticity

Huo Yongzhong

1996, 17(10): 909-917.

Abstract(2080) PDF(441)

Abstract:
Solid-solid phase transitions often exhibt hysteresis and to describe the hysteretic behavior we need infernal variables. For shape memory single crystal under uni-axial tensile loading the internal variable has been identified experimentally as the number of interfaces between the austenitic and the martensitic phase regions. Experimental evidences are discussed here. Thermodynamical modelling based ont he internal variable is presented.

The Linear Bi-Spatial Tensor Equation φ_ijAⁱXB^j=C

Chen Yuming, Xiao Heng

1996, 17(10): 919-926.

Abstract(2452) PDF(455)

Abstract:
A linear bi-spatial tensor equation which contains many of ten encotuntered equations as particular cases is thoroughly studied Explicit solutions are obtained. No conditions on eigenvalues of coefficient tensors are imposed.

Degenerate Parabolic Equation and Unilateral Constraint Systems

Guo Xingming

1996, 17(10): 927-932.

Abstract(2142) PDF(440)

Abstract:
In this paper the existence and regularity of solution to a nonlinear and nonautonomous multivalued parabolic equation which represents some energy dissipative problms with nonlinear constiutive constraints and non-differential external constraints in physics mechanics and optimization.

A New Method for the Construction of Integrable Hamiltonian Systems

Gao Puyun

1996, 17(10): 933-938.

Abstract(1922) PDF(463)

Abstract:
A new method for the construction of integrable Hamiltonian system is proposed.For a given Poisson manifold the present paper constructs new Poisson brackets on it by making use of the Dirac-Poisson structure([1]),and obtains, further new integrable Hamiltonian systems. The constructed Poisson bracket is usual non-linear, and this new method is also different from usual ones([2-4]).Two examples are given.

Geometric Framework and Minimal Realizations of Nonlinear Systems on Fibre Bundle

Mu Xiaowu

1996, 17(10): 939-950.

Abstract(2141) PDF(461)

Abstract:
The definition of nonlinear control sysms on fibre bundles proposed by Brockett and Willems is incomplete from the mathematical view geometric framework is proposed and a minimal realization theory is developed for nonlinear control systems on fibre bundles which is elaborated as a natural generalization of Sussmann's theory and differs essentially from Van der Schaft's approach. Limitations of realization theory given by Van der Schaft are also discussed.