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1999年 第20卷 第5期    刊出日期：1999-05-18

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论文

DYNAMICAL EQUATIONS FOR POLAR CONTINUA IN ORTHOGONAL CURVILINEAR COORDINATES

戴天民;宋彦琦

1999, 20(5):  465-468. 

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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 the help of the anholono mic physical frame method are derived.

THE METHOD OF ANALYSIS OF CRACK PROBLEM IN THREE- DIMENSIONAL NO N-LOCAL EL ASTICITY

赵明皞;程昌钧;刘元杰;刘国宁;张石山

1999, 20(5):  469-475. 

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In this paper, the displacement discontinu ity 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 inte gralequation (DDBIE) and boundary-element method (DDBEM) of local (classical) elasticity, a method of analysis of crack in 3D non-local elasticity with wide application is proposed with the DDFS. Through 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

陈良森;赵兴华

1999, 20(5):  476-484. 

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In this paper, the theory of materi als 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 s tress as the "center" of the yield surface in the Cauchy space. The back stres s tensor is Lagrangian,and must be defined in the Lagrangian stress space.

THE BEST APPROXIMATION AND COINCIDENCE THEOREMS FOR COMPOSITES OF ACYCLIC MAPPINGS

丁协平

1999, 20(5):  485-494. 

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Some new coincidence theorem s involving a new class of set-valued mappings containing composites of acyclic mappings defined in a contractible space are proved. For 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 theorems in this paper.

RESEARCH ON THE PARTICLE DISPERSION IN THE PARTICULATE TWO-PHASE ROUND JET

林建忠;林江;朱丽兵

1999, 20(5):  495-502. 

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In this paper, the three-dimensional vo rtex 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 motio n based on the computed flows. The results show that the particle motion is affe cted 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, part icles disperse wider along radial direction, which conforms to the experimental results. The degree of particle dispersion is in the direct ratio to the amplitu de of perturbation. The conclusions given in the paper are useful to the practic e usage.

INFLUENCE OF INITIAL IMPERFECTION AND COUPLING BETWEEN BENDING AND EXTENSION ON VIBRATION, BUCKLING AND NONLINEAR DYNAMIC STABILITY OF LAMINATED PLATES

王列东;刘正宁;周承倜

1999, 20(5):  503-512. 

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

ANALYSIS OF THE SECONDARY STABILITY OF COMPRESSIBLE BOUNDARY LAYER FLOWS OVER A TWO-DIMENSIONAL PLATE

范绪箕;楼卓时

1999, 20(5):  513-518. 

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This paper used the Floquet’s 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.

A NOVEL SOLUTION OF TOROIDAL SHELLS UNDER AXISYMMETRIC LOADING

张若京

1999, 20(5):  519-526. 

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Several improvements are made for existing asymptotic expansions for the axisymmetric toroidal shells. The new expansions are numerically satisfactory 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 this paper, three particular solutions are given, one of which is just the solution obtaine d by Tumarkin (1959) and Clark(1963).

SUPER NONLINEAR TOTAL ENERGY OF A PARTICLE AND THE THEORY OF DE BROGLIE WAVE

杨文熊;杨长俊

1999, 20(5):  527-531. 

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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 reste nergy 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 light c.

A CATENARY ELEMENT FOR THE ANALYSIS OF CABLE STRUCTURES

彭卫;孙炳楠;唐锦春

1999, 20(5):  532-534. 

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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 g₀/cos²θ

潘岳;戚云松

1999, 20(5):  535-544. 

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In this paper, after taking the effect of axis force on bending into consideration, the general potential energy for the circular double articulated arch is established undergoing vertical distributive load g₀/cos²θ. With sufficient engineering precision, the fourth approximations to the destabilizing critical load of the arch under t his load are obtained by Ritz method. The approximations to the critical load ta ble 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

何吉欢

1999, 20(5):  545-556. 

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In this paper, it has been pro ved that the well-known Hu-Washizu variational principle is a pseudo-generalized variational principle (pseudo-GVP). The stationary conditions of its functional may satisfy all its field equations and boundary conditions if all the variables in the functional are considered as independent variations, but 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 constraints of stress-strain relations.

SIMULATION AND STUDY OF THE MODULUS OF ELASTICITY OF NANOCRYSTALLINE MATERIALS

孙伟;常明;杨保和

1999, 20(5):  557-563. 

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In this paper, a molecular dynamics simulations are provided for atomic structure of nanocrystals (1～3nm) by which the lattice parameter of X-ray diffraction, 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

徐振铎;刘尔烈

1999, 20(5):  564-567. 

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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 the n 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

张英世

1999, 20(5):  568-578. 

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Differential equations of free/forced vibrations of stepped rectangular thin plates on Winkler’s foundation are estab lished 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 S YSTEM

李永昆

1999, 20(5):  579-584. 

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In this paper, the existence o f a positive periodic solution to the following neutral predator-prey system is studied,in which r,a₂,K and τ are positive constants, and a₁(t),α(t),b(t) and β(t) are positive continuous functions of period ω.