应用数学和力学

1999 Vol. 20, No. 5

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Dynamical Equations for Polar Continua in Orthogonal Curvilinear Coordinates

Dai Tianmin, Song Yanqi

1999, 20(5): 441-444.

Abstract(2288) PDF(915)

Abstract:
In this paper the concrete forms of dynamical equations for finite deformable polar elastic media of Boussinesq type,Kirchhoff type,Signorini type and Novozhilov type with help of the anholonomic physical frame method are derived.

The Method of Analysis of Crack Problem in Three-Dimensional Non-Local Elasticity

Zhao Minghao, Cheng Changjun, Liu Yuanjie, Liu Guoning

1999, 20(5): 445-451.

Abstract(2059) PDF(635)

Abstract:
In this paper,the displacement discontinuity fundamental solution(DDFS) corresponding to the unit concentrated displacement discontinuity for three dimensional(3D) non-local elasticity under symmetrical condition is obtained.Based on the displacement discontinuity boundary integral-equation(DDBIE) and boundary-element method(DDBEM)of local(classical) elasticity,a method of analysis of crack in 3D non-local elasticity with a generalized application is proposed with the DDFS. By use of the method,several important problems of fracture mechanics are analysed.

A Mathematical Theory of Materials with Elastic Range and the Definition of Back Stress Tensor

Chen Liangsen, Zhao Xinghua

1999, 20(5): 452-460.

Abstract(2894) PDF(1087)

Abstract:
In this paper,the theory of materials with elastic range by Lucchesi and Podio-Guidugli (1988) has been generalized.It has also shown that there are some difficulties on the definition of back stress as the"center" of the yield surface in the Cauchy space.The back stress tensor is Lagrangian,and must be defined in the Lagrangian stress space.

Best Approximation and Coincidence Theorems for Composites of Acyclic Mappings

Ding Xieping

1999, 20(5): 461-469.

Abstract(2213) PDF(593)

Abstract:
Some new coincidence theorems involving a new class of set-valued mappings containing composites of acyclic mappings defined on a contractible space are proved.As applications,some best approximation theorems and coincidence theorems for set-valued mappings are also given.A number of known results in recent literature are improved and generalized by the thorems in this paper.

Research on the Particle Dispersion in the Particulate Two-Phase Round Jet

Lin Jianzhong, Lin Jiang, Zhu Libing

1999, 20(5): 470-476.

Abstract(2645) PDF(668)

Abstract:
In this paper,the three-dimensional vortex filament method was used to simulate the evolution of vortex structures in the axisymmetric round jet.The results agree well with the ones given by Chung and Troutt.Then one-coupling model was employed to calculate the particle motion based on the computed flows.The results show that the particle motion is affected by flows obviously at the case of particle number St 1 and negligibly at St 1,particles distribute around the vortex structures uniformly at St~1.When perturbations with wavenumber 5 are introduced to vortex rings, particles disperse wider along radial direction,which conforms to the experimental results.The degree of particle dispersion is in the direct ratio to the amplitude of perturbation.The conclusions given in the paper are useful to the practice usage.

Influence of Initial Imperfection and Coupling Between Bending and Extension on Vibration, Buckling and Nonlinear Dynamic Stability of Laminated Plates

Wang Liedong, Liu Zhengning, Zhou Chengti

1999, 20(5): 477-485.

Abstract(1955) PDF(740)

Abstract:
In this paper,the influence of initial imperfection and coupling between bending and extension on vibration,buckling and nonlinear dynamic stability of laminated plates is studied.The governing equation is derived.It is a nonlinear modified Mathieu Equation.Numerical solutions of 5 typical composite materials namely,Scotch-1002,Kevlar-49,B4/5505,T300/5208 and AS/3501 are computed. Results reveal that the existence of initial imperfection and coupling effect,make plates much more sensitive to entering parametric resonance with amplitude greater than that of perfect plates.Coupling effect for different laminates,especially,for that with few layers,is different.If coupling effect is neglected,design of plate structures for buckling and dynamic stability would be unconservative for more than 10%.

Analysis and Calculation of Secondary Instability of Two-Dimensional Compressible Boundary Layer Flows of A Plate

Fan Xuji, Lou Zhuoshi

1999, 20(5): 486-490.

Abstract(2830) PDF(663)

Abstract:
Thia paper used the Floquets three-dimensional linear stability theory in the analysis of two-dimensional compressible boundary layer,a set of stability equations is constructed,the effect of three dimensional linear small perturbation on the two-dimensional compressible boundary layer transition is studied,and the effect of coming flow Ma number on growth and development of the subharmonics is calculated.It can be seen from the calculations,the effect caused by the interaction of two-dimensional and three-dimensional perturbation waves on the development of two-dimensional compressible laminar boundary layer.

Novel Solutions of Toroidal Shells Under Axisymmetric Loading

Zhang Ruojing

1999, 20(5): 491-498.

Abstract(2390) PDF(523)

Abstract:
Several improvements are made for existing asymptotic expansions for the axisymmetric toroidal shells.The new expansions are numerically satisfaytory and satisfy the accuracy of the theory of thin shells.All of them are expressed in terms of generalized Airy functions,instead of Bessel or Airy function for the homogeneous and Lommel function for the particular solutions,respectively,as in the existing work.In fact,three particular solutions are given in the paper,one of which is just the solution obtained by Tumarkin(1959) and Clark(1963).

Super Nonlinear Total Energy of a Particle and the Theory of de Broglie Wave

Yang Wenxiong, Yang Changjun

1999, 20(5): 499-503.

Abstract(2143) PDF(614)

Abstract:
By using Laurent series,the velocity(~c)is expanded and then the total energy expression of a particle moving with high velocity is obtained.The total energy contains two parts:the rest energy and the kinetic energy.Also in this paper the theory of the de Broglie wave from the relation of the energy-momentum is obtained in which the phase velocity is still less than the velocity of lightc.

A Catenary Element for the Analysis of Cable Structures

Peng Wei, Sun Bingnan, Tang Jinchun

1999, 20(5): 504-506.

Abstract(2443) PDF(864)

Abstract:
Based on analytical equations,a catenary element is presented for the finite element analysis of cable structures.Compared with usually used element(3-node element,5-node element),a program with the proposed element is of less computer time and better accuracy

The Solution to the Destabilizing Critical Load of Circular Double Articulated Arch Under Going Vertical Distributive Load g 0/ cos²θ

Pan Yue, Qi Yunsong

1999, 20(5): 507-514.

Abstract(2089) PDF(572)

Abstract:
In this paper,after taking the effect of axis force on bending into consideration,the general poteneial energy for the circlular double articulated arch is established undergoing vertical distributive load g0/cos²θ.With sufficient engineering precision,the fourth approximations to the destablizing critical load of the arch under this load are obtained by Ritz method.The approximations to the critical load table are listed for various center angles of arch,and are contrasted with the critical load circular arch undergoing radial uniform load.Some reference results have been obtained.

Further Study of the Equivalent Theorem of Hellinger- Reissner and Hu-Washizu Variational Principles

He Jihuan

1999, 20(5): 515-524.

Abstract(3873) PDF(830)

Abstract:
In this paper,it is proved that the well-known Hu-Washizu variational principle is a pseudo- generalized variational principle(pseudo-GVP),which is a functional whose stationary conditions would satisfy all its field equations and boundary conditions if all the variables in the functional were considered as independent variations,but in fact there might exist some kinds of constraints.Some new pseudo-GVPs are established to distinguish them from genuine ones by the so-called inverse Lagrange multiplier method.The constrained Hu-Washizu principle,therefore,is proved to be equivalent with the Hellinger-Reissner principle under the same constraints of stress-strain relations.

Simulation and Study of the Modulus of Elasticity of Nanocrystalline Materials

Sun Wei, Chang Ming, Yang Baohe

1999, 20(5): 525-530.

Abstract(2483) PDF(724)

Abstract:
In this paper a molecular dynamics simulations for atomic structure of nanocrystals(1-3nm) by which the lattice parameter of X-ray diffraction are provided,cohesive energy and modulus of elasticity were computed.The results show that the structure of grain and grain boundaries in the same in both nanocrystal and coarse grain materials.The decrease of grain size and the increase volume fraction of grain boundaries lead to a series of different features,the modulus of elasticity of nanocrystalline materials have been found to be much reduced.

Equilibrium Stability of Generalized Birkhoff’s Autonomous System

Xu Zhenduo, Liu Erlie

1999, 20(5): 531-534.

Abstract(2415) PDF(646)

Abstract:
In this paper,equilibrium stability of generalized Birkhoff's autonomous system is discussed.First,equilibrium equations of generalized Birkhoff's Autonomous system are set up,and then the linear approximate method and direct method of stability in equilibrium state are studied. Some results on equilibrium of generalized Birkhoff's autonomous system are obtained on the basis of Lyapunov's thorem.Last,the application of the results is illustrated with an example.

Vibrations of Stepped Rectangular Thin Plates on Winkler’s Foundation

Zhang Yingshi

1999, 20(5): 535-544.

Abstract(2635) PDF(530)

Abstract:
Differential equations of free/forced vibrations of stepped rectangular thin plates on Winkler's foundation are established by using singular functions,and their general solutions are also solved for expression of vibration mode function and frequency equations on usual supports derived with Woperator,as well as forced responses of such plates under different-type loads discussed with Fourier expansion of generalized functions.

Positive Periodic Solution of a Neutral Predator-Prey System

Li YongKun

1999, 20(5): 545-550.

Abstract(2524) PDF(603)

Abstract:
In this paper,the existence of a positive periodic solution to the following neutral predator-prey systemis studied,in whichr,a₂,K and τ are positive constants,and a1(t),A(t),b(t)and β(t)are positive continuous functions of period ω.