应用数学和力学

1991 Vol. 12, No. 3

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The Re-examination of the Weakly Nonlinear Theory of Hydrodynamic Stability

Zhou Heng

1991, 12(3): 203-208.

Abstract(2865) PDF(576)

Abstract:
The weakly nonlinear theory has been widely applied in the problem of hydrodynamic stability and also in other fields. However, although its application has been successful for some problems, yet, for other problems, the results obtainedhre not satisfactory, especially for problems like transition or the evolution of the vortex in the free shear flow, for which the goal of the theoretical investigation is not seeking for a steady state, but predicting an evolutional process. In this paper, we shall examine the reason for the unsuccessfulness and suggest ways for its amendment.

Generalized Variational Principles on Nonlinear Theory of Elasticity with Finite Displacements

Hsueh Dah-wei

1991, 12(3): 209-218.

Abstract(2195) PDF(795)

Abstract:
Two generalized variational principles on nonlinear theory of elasticity with finite displacements in which the σ_ij_i e_ij and u_i are all three kinds of independent functions are suggested in this paper. It is provedthat these two generalized variational principles are equivalent to each other if the stress-strain relation is satisfied as constraint. Some special cases, i.e. generalized variational principles on nonlinear theory of elasticity with small deformation, on linear theory with finite deformation and on linear theory with small deformation together with the corresponding equivalent theorems are also obtained. All of them are related to the three kinds of independent variables.

An Exponentially Fitted Difference Scheme for the Hyperbolic-hyperbolic Singularly Perturbed Initial-Boundary Value Problem

Su Yu-chcng, Lin Ping

1991, 12(3): 219-227.

Abstract(2799) PDF(505)

Abstract:
In this paper we discuss, an initial-boundary value problem of hyperbolic type with first derivative with respect to x. The asymptotic solution is constructed and its uniform validity is proved under weader compatibility conditions. Then we develop an exponentially fitted difference scheme and establish discrete energy inequality. Finally, we prove that the solution of difference problem uniformly converges to the solution of the original problem.

Energy Principle of Large Deformation for Living Systems

Chen Zhi-da

1991, 12(3): 229-235.

Abstract(2129) PDF(397)

Abstract:
Living system is a non-equilibrium open system having the function of self-organization and self-control. The study of energy principle of living system involves two principal parts: mechanics and thermodynamics. The classical infinitesimal deformation theory and thermodynamics of equilibrium state are not sufficient to explain the complex motion of living system. We aim in this paper to describe the mechanical energy principle of macroscopic motion of living body based on large deformation non-symmetry stress field theory. The principle of irreversible thermodynamics applied to livihg system will be left in another paper^[9].

Generalization of the Method of Full Approximation and Its Applications

Dai Shi-qiang

1991, 12(3): 237-244.

Abstract(2611) PDF(634)

Abstract:
This paper presents a generalized form of the method of full approximation. By using the concept of asymptotic linearization and making the coordinate transformations including the nonlinear functionals of dependent variables, the original nonlinear problems are linearized and their higher-order solutions are given in terms of the first-term asymptotic solutions and corresponding transformations. The analysis of a model equation and some problems of weakly nonlinear oscillations and waves with the generalized method shows that it is effective and straightforward.

The Transient Two-Dimensionai Flow through Double Porous Media

Liu Ci-qun

1991, 12(3): 245-249.

Abstract(2120) PDF(552)

Abstract:
This paper presents the analytical solutions in Laplace domain for two-dimensional nonsteady flow of slightly compressible liquid in porous media with double porosity by using the methods of integral transforms and variables separation. The effects of the ratio of storativities ω, interporosity flow parameter λ on the pressure behaviors for a vertically fractured well with infinite conductivity are investigated by using the method of numerical inversion. The new log-log diagnosis graph of the pressures is given and analysed.

On the Nonlinear Stability of Symmetrically Laminated Cylindrically Orthotropic Shallow Spherical Shells

Liu Ren-huai

1991, 12(3): 251-258.

Abstract(2309) PDF(546)

Abstract:
In this paper, the large deflection theory of symmetrically laminated cylindrically orthotropic shallow spherical shells is established. Based on this theory, applying the modified iteration method, the analytic solution for critical buckling loads of the shells with rigidly clamped edges under actions of uniform pressure has been obtained.

A Singular Perturbation Problem for Periodic Bounday Partial Differentia! Equation

Lin Peng-cheng, Jiang Ben-xian

1991, 12(3): 259-268.

Abstract(2568) PDF(449)

Abstract:
In this paper, we consider a singular perturbation elliptic-parabolic partial differential equation for periodic boundary value problem, and construct a difference scheme. Using the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, we prove that the scheme constructed by this paper converges uniformly to the solution of its original problem with O(r+h²).

The Threo-Dimensional Analysis of the Self-Vib rational Characteristics of the 2050mm Hot-Strip Mill Housing by Means of Laser Holographic Interferometry and Finite Element Method

Liu Wei-jian, Jiang Wei-xing, Qu Zhi-hao

1991, 12(3): 269-277.

Abstract(2263) PDF(385)

Abstract:
According to the theory of similarity, a three-dimensional simulation study on the self-vibrational characteristics of the 2050mm hot-strip finishing mill housing at Baoshan Iron and Steel Complex has been carried out. The analysis of the main vibrational modes of the first three orders has also been done by means of holographic interferometry. In addition, the authors have carried out the numerical analysis of finite elements in three dimensions. The comparison of the results of both analyses (simulation analysis and numerical analysis of finite element) shows that they are consistent.

Thermal-Bucking of Thin Annular Plates under Multiple Loads

Li Shi-rong, Cheng Chang-jun

1991, 12(3): 279-286.

Abstract(2455) PDF(502)

Abstract:
On the basis of Von Karman equations, the thermal-buckling of thin annular plates subjected to a field of non-uniform axisymmetric temperature and a variety of boundary conditions is discussed. The linearized problem is analyzed and stability boundaries which characterize instability of oplate are obtainedby means of numerical and analysis methods.

A Novel Method of Solving the Exact Equations for Capillary-Gravity Waves

Zou Qi-su, Chen Yao-song, Qian Bao-Yuan

1991, 12(3): 287-290.

Abstract(2889) PDF(536)

Abstract:
A new method is presented for the computation of two-dimensional periodic progressive surface waves propagating under the combined influence of gravity and surface tension. The nonlinear surface is expressed by Fourier series with finite number of terms, after the computational domain is transformed into a unit circle. The dynamic boundary equation is used in its exact nonlinear form and the coefficients of Fourier series are found by the Newton-Raphson method successively. This is a neat method, Yielding high prescision with little computational effort.

Asymptotic Solutions of the Nonlinear Stability of a Truncated Shallow Spherical Shell under a Concentrated Load

Kang Sheng-liang

1991, 12(3): 291-302.

Abstract(2472) PDF(574)

Abstract:
In this paper, the nonlinear stability problem of a clamped truncated shallow spherical shell with a nondeformable rigid body at the center under a concentrated load is studied by means of the singular perturbation method. When the geometrical parameter k is large, the uniformly valid asymptotic solutions are obtained.