应用数学和力学

1985 Vol. 6, No. 9

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Incremental Formulation for Finite Strain and Finite Rotation of Continuum Mechanics

Chen Zhi-da

1985, 6(9): 769-774.

Abstract(1787) PDF(1028)

Abstract:
Due to some confusions existing in the current coordinate description of large rotation and large strain of continuum mechanics, there are always undiscernible mistakes in the formulation of finite element method for large displacement problems. The object of this paper is to scrutinize some basic theoretical point of views in continuum mechanics of finite deformation by the author's geometrical field theory^[1][2], and to formulate fundamental equations of incremental displacement for finite element method by the energy principle of power type. The method described was used by Y. Shang^[9] and H. P. Xie^[10]. They obtained results which are in very good agreement with experiments of large deformation.

Singular Perturbations of Robin Boundary Value Problems for Semilinear Systems

K. W. Chang, Lin Zong-chi

1985, 6(9): 775-779.

Abstract(1628) PDF(602)

Abstract:
In this paper, we study the singular perturbations of Robin boundary value problems for semilinear systems using the method and technique of differential inequalities. We assume that the corresponding reduced system has at least one solution which is I_q-stable. This "component-wise" I_q-stability condition will allow us to obtain estimates for each component of the solution.

Correspondence Function D(z) and Generalized Irregular Equations

Dong Ming-de

1985, 6(9): 781-790.

Abstract(1667) PDF(581)

Abstract:
Extending Riemann's idea of P function (using equation's parameters to represent the function defined by the equation), we introduce correspondence functions D(z) to describe regular and irregular integrals in a unifying way. By explicit solution discuss monodromy group of non-Fuchsian equations. The explicit expressions of exponent and expansion coefficients for Floquet solution are obtained. Method of correspondence functions permits us to obtain systematically the solutions of generalized irregular equations, having regular, irregular poles, essential, algebraic, transcendental, logarithmic singularities as well as singular line. The representation of basic set of solutions by D_σ(z) function makes it possible to enlarge the scope of investigation of analytic theory. The significance of Poincare's conjecture is discussed, as D functions are automorphic.

General Solution of Elastodynamics

Shen Hui-chuan

1985, 6(9): 791-796.

Abstract(1707) PDF(619)

Abstract:
The elastodynamic problem is investigated via stokes-Helmholtz separation of the vector with time, and the general solutions of Lame equation are derived. The medium is assumed to be homogeneous and isotropic.

Two-Dimensional Numerical Analysis of Stress-Wave-Amplifier

Zhou Guang-quan, Liu Xiao-min

1985, 6(9): 797-806.

Abstract(1642) PDF(527)

Abstract:
Using dynamic finite element method, the propagation of stress waves in two-dimensional conically shaped stress-wave-amplifiers is analysed. The effects of geometrical factors, input-pulse shape and pulse rising time on amplifying multiplication and wave shape of transmission waves are discussed. The consistency between numerical results and experimental results based on Hopkinson bar is satisfactory. The numerical accuracy is inploved comparing with the characteristic method.

Analytical Solutions for the Selfsimilar Problems of Viscous Fluid Flow

Yuan Yi-wu

1985, 6(9): 807-812.

Abstract(1434) PDF(444)

Abstract:
This paper presents a step-by-step approximating method to obtain the analytical solutions of the differential equations for the self-similar problems of viscous fluid flow (1.1-1.4). Prosnak (1969) obtained solutions of these equations by using a small parameter method, but he reduced the governing equations to the linear differential equations with constant coefficients.

On Equivalents of the Reciprocal Theorem to Superposition Principles

Fu Bao-lian

1985, 6(9): 813-818.

Abstract(1910) PDF(751)

Abstract:
In this paper in the terms of theory we have proved that the reciprocal theorem is equivalent to the superposition principle of displacements and is equivalent to the superposition principle of reactive forces. These equivalents have important theoretical values and practical values. At the same time we also point out that Castigliano's displacement equation can be applied to solve the interior displacement of the region of the deformable body too.

Nonlinear Bendings of Rectangular Symmetrically Laminated Cross-Ply Plates under Various Supports

Zhou Ci-qing

1985, 6(9): 819-832.

Abstract(1519) PDF(593)

Abstract:
This paper studies the nonlinear bendings of rectangular symmetrically laminated cross-ply plates subjected to uniform pressure under various supports on the basis of^[3] by the singular perturbation method offered in^[1]. The uniformly valid N-order asymptotic solutions of the deflection and stress function are derived. Analyses and numerical solutions are given for simply supported rectangular laminates, whase edge displacement is vanished.

The Finite Element Analysis of the Flexible Beams and Plates

Liu Zheng-xing, Wu Lian-yuan, Feng Tai-hua

1985, 6(9): 833-844.

Abstract(1849) PDF(493)

Abstract:
This paper studies large deflection problem of beam and plates by the finite element method. The elongation of the middle surface caused by its rotation is considered in strain-displacement relations. The higher order terms will be reserved when strain energy is calculated. The elastic stiffness matrix, linear and nonlinear initial stress stiffness metrices are derived by the principle of minimum potential energy. Examples show that precision will be properly manifested although the total storage amount and the calculating lime are not increased. The iterative method with co-moving coordinate must be adopted to avoid parasitic rigid body motion.

Perfectly Plastic Stress Field at a Mixed-Mode Crack tip Under Plane and Anti-Plane Strain

Lin Bai-song

1985, 6(9): 845-852.

Abstract(1662) PDF(572)

Abstract:
Under the condition that any perfectly plastic stress component at a crack tip is nothing but the function of θ only, making use of equilibrium equations, stress-strain-rate relations, compatibility equations and yield condition, in this paper, we derive the general analytical expressions of the perfectly plastic stress field at a Mixed-Mode crack tip under plane and anti-plane strain. Applying this general analytical expressions to the Mixed-Mode cracks, we can obtain the analytical expressions of perfectly plastic stress fields at the tips of Mixed-Mode Ⅰ-Ⅲ,Ⅱ-Ⅲ and Ⅰ-Ⅱ-Ⅲ cracks.

Discussion of "Some Discussions on Finite Deformation of Continuous Media"

Peng Len-sheng, Cheng Yuan-sheng

1985, 6(9): 853-857.

Abstract(1496) PDF(516)

Abstract: