应用数学和力学

1989 Vol. 10, No. 4

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On Necessary Conditions for Resonance in Turning Point Problems for Ordinary Differential Equations

Jiang Fu-ru

1989, 10(4): 277-284.

Abstract(1799) PDF(526)

Abstract:
In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of necessary conditions for resonance has been offered.

On the Stability of Distorted Laminar Flow(Ⅲ)——The Nonlinear Stability Analysis of Distorted Parallel Shear Flow

Zhou Zhe-wei

1989, 10(4): 285-295.

Abstract(1750) PDF(613)

Abstract:
Based on the hydrodynamic stability theory of distorted laminar flow and the kind of distortion profiles on the mean velocity in parallel shear flow given in paper [1], this paper investigates the nonlinear stability behaviour of parallel shear flow, carries on stability calculation taking account of the perturbations of background turbulence noise under certain assumption, and obtains some results in accordance qualitatively with those of experiment for plane Poiseuille flow and pipe Poiseuille flow.

Application of the Method of the Reciprocal Theorem to Finding Displacement Solutions of Cubes

Fu Bao-lian

1989, 10(4): 297-308.

Abstract(2040) PDF(715)

Abstract:
In this paper the method of reciprocal theorem is extended to find solutions of three-D problems of elasticity.First we give the basic solution of the cube with six surfaces fixed as the basic system and then using the reciprocal theorem between the basic system acted on by unit concentrated loads and the actual system with prescribed surface displacements, we find displacement solution of the actual system.

Wave Propagation with Mass-Coupling Effect in Fluid-Saturated Porous Media

Li Xiang-wei, Li Xiang-yue

1989, 10(4): 309-314.

Abstract(1491) PDF(710)

Abstract:
This article utilizes the theory of mixtures to formulate a general theory of wave propagation with mass-coupling effect in fluid-saturated porous media.An attempt is made to discuss the physical interpretation and the thermodynamic restriction of the coefficients appearing in the equations obtained, by the comparison it is shown that Biot's classical theory and the present one are essentially consistent.Also wave velocities in some special cases are calculated, from which it is concluded that mass-coupling and permeability of media greatly affect wave propagation behavior.

Diagonalization Method for a Singularly Perturbed Vector Robin Problem

Ni Shou-ping

1989, 10(4): 315-322.

Abstract(1559) PDF(571)

Abstract:
In this paper the method and technique of the diagonalization are employed to transform a vector second-order nonlinear system into two first-order approximate diagonalized systems.The existence and the asymptotic behavior of the solutions are obtained for a vector second-order nonlinear Robin problem of singular perturbation type.

A Viscoplastic Model Based on No-Yierd-Surface Concept

Zhou Guang-quan, Cheng Jing-yi

1989, 10(4): 323-330.

Abstract(1878) PDF(498)

Abstract:
The elastic/viscoplastic constitutive equation which describes deformation law of metal materials was suggested based on no-yield-surface concept and thermal activation theory of dislocation.The equation which takes account of effects of strain-rate, strain history, strain-rate history, hardening and temperature has stronger physical basis.Comparison of the theoretical prediction with experimental results of mechanical behaviours of Ti under conditions of uniaxial stress and room temperature shows good consistency.

Bending and Vibration of Composite Laminated Plates

Deng Liang-bo

1989, 10(4): 331-338.

Abstract(1687) PDF(612)

Abstract:
Hybrid-stress finite element method is applied for analysis of bending and vibration of composite laminated plates in this paper.Firstly,based on the modified-complementary principle,a reciangular hybrid-stress plate bending element is presented which applies to analysis of laminates.Inside the element,different stress parameters are assumed according to different layers.The boundary displacements are determined by means of theassumption of YNS theory on the boundary of elements.The element formed in this way not only can take effects of transverse shear deformation and local warping into account,but also has less degrees of freedom.Then.problems of bending and vibration of laminates aresolved by using this element.and the numerical results are compared with the exact solutions.This shows that the results obtained in the paper are very close to the exactresults.

A Class of Variational Difference Schemes for a Singular Perturbation Problem

Lin Ping

1989, 10(4): 339-345.

Abstract(1697) PDF(623)

Abstract:
In this paper, a singularly perturbed boundary value problem for second order self-adjoint ordinary differential equation is discussed.A class of variational difference schemes is constructed by the finite element method.Uniform convergence about small parameter is proved under a weaker smooth condition with respect to the coefficients of the equation.The schemes studied in refs.[1], [3], [4] and [5] belong to the cllass.

Generalized Transfer Function of Control System and an Improvement on the Decision Method of Movement Stability

Ye Shou-zhen, Sha Wan-qian

1989, 10(4): 347-357.

Abstract(1825) PDF(529)

Abstract:
In this paper the definitions of generalized transfer function of control system and its continuity are presented.Using generalized transfer function as a tool,a set of theorems fordeciding movement stability have been constructed.Thus basing understanding of the characteristics of a control dynamics system on its measured procedure will simplify the decision method of movement stability problems.

Perturbation Analysis for the Postbucfcling of Rectangular Orthotropic Plates

Shen Hui-shen

1989, 10(4): 359-370.

Abstract(1874) PDF(627)

Abstract:
In this paper, applying perturbation method to von Karman-type nonlinear large deflection equations of orthotropic plates by taking deflection as perturbation parameter, the postbuckling behavior of simply supported rectangular orthotropic plates under in-plane compression is investigated.Two types of in-plane boundary conditions are now considered and the effects of initial imperfections are also studied.Numerical results are presented for various cases of orthotropic composite plates having different elastic properties.It is found that the results obtained are in good agreement with those of experiments.

1989, 10(4): 371-371.

Abstract(1548) PDF(764)

Abstract: