复合材料层板分层伴以横向裂纹扩展的三维有限元分析

本文采用三维有限元模型,对典型铺设的[0_2/±45_2/90_2]_s碳/环氧复合材料层板中分层伴以横向裂纹的产生和扩展导致的层间应力分布进行了分析。计算结果表明层间裂纹首先在90°层中部出现并开裂至相邻界面处而产生横向裂纹,横向裂纹的出现引起局部分层按三角形状扩展;并指出分层损伤过程是一个主导性的稳定扩展过程,这是导致刚度下降的主要因素。最后,数值计算结果与实验结果比较,两者是吻合的。     

Stress in transversely isotropic half-space with typical loads acting on its surface

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Transverse Decay of Solutions in an Elastic Cylinder

In a semiinfinite cylinder composed of anisotropic linearised elastic material, loaded on the base and clamped along the lateral surface, it is known that the solution as measured, for example, by the strainenergy flux through a plane crossection decays longitudinally at most exponentially with respect to the axial distance from the base. There is, however, also a transverse radial decay of the solution, again measured for example by the strainenergy, occurring from the region close to the cylinder's axis to the region near the lateral surface, where the energy vanishes.This problem is considered in the present paper which discusses a circular semiinfinite cylinder and derives an estimate for the strainenergy contained in a cylindrical annulus at a given distance from the base and of variable height, and whose outer surface coincides with the lateral surface of the cylinder. It is shown that the strainenergy decays at most algebraically to zero as the inner radius of the annulus increases to that of the cylinder.Sommario. E'noto che in un cilindro semiinfinito composto da materiale elastico lineare anisotropo, caricato sulla base ed incastrato lungo la superficie laterale, la soluzione elastica, misurata, per esempio, dal flusso di energia di deformazione attraverso una sezione trasversale piana, decade con legge al più esponenziale con la distanza dalla base. C'è tuttavia, anche un decadimento radiale della soluzione, misurato, per esempio, dall'energia di deformazione che passa dalla regione vicina all'asse del cilindro a quella vicin alla superficie laterale dove l'energia si annullaQuesto problema è qui studiato. Si discute in particolare un cilindro circolare semiinfinito e si deduce una stima per l'energia di deformazione contenuta in un anello cilindrico ad una distanza assegnata dalla base e di altezza variabile, e la cui superficie esterna coincide con la superficie laterale del cilindro. Si dimostra che l'energia di deformazione decade al più con legge algebrica a zero quando il raggio interno del cilindro si avvicina a quello esterno.     

Transient torsional wave propagation in a transversely isotropic tube

Summary By use of the separation of variables method and the Laplace transformation, the two-dimensional transient torsional wave propagation problem in a transversely isotropic tube is studied when a torque is suddenly applied to its end surface. The results show that, for the discontinuous distribution of the impact shear stress, the region of the 2D stress distribution in a transversely isotropic tube becomes large with the increase of the anisotropy of the material. Received 13 June 1997; accepted for publication 17 June 1998     

State vector solutions for nonaxisymmetric problem of multilayered half space piezoelectric medium

A state space formulation is established for the nonaxisymmetric space problem of transversely isotropic piezoelectric media in a system of cylindrical coordinate by introducing the state vector. Using the Hankel transform and the Fourier series, the state vector equations are transformed into ordinary differential equations. By the use of the matrix methods, the analytical solutions of a single piezoelectric layer are presented in the form of the product of initial state variables and transfer matrix. The applications of state vector solutions are discussed. An analytical solution for a semiinfinite piezoelectric medium subjected to the vertical point forceP _z, horizontal point forceP _x along x-direction and point electric charge Q at the origin of the surface is presented. According to the continuity conditions at the interfaces, the general solution formulation forN-layered transversely isotropic piezoelectric media is given. Project supported by the National Natural Science Foundation of China (Grant No. 59648001).     

极端相对论性正负电子对等离子体中横振荡的色散关系

 由伏拉索夫方程和费米分布函数的相对论性修正形式推导出相对论性正负电子对等离子体中横波的色散方程,对等离子体中的横波进行解析研究,得到长波支和短波支的色散关系。从解析的色散曲线发现了与Mikhailovskii在极端相对论性情况下对于电子-离子等离子体中色散关系研究相类似的结果:在极端相对论性等离子体中横波的解析色散曲线具有不连续性。基于解析色散曲线的不连续性,进而采用数值计算的方法求解了完整的等离子体色散方程,得到其数值解,数值色散曲线可将解析上的长波和短波衔接起来,使其成为一条完整的色散曲线。     

Experimental study on the local similarity scaling of the turbulence spectrum in the turbulent boundary layer

The streamwise fluctuating velocity in the turbulent boundary layer is measured under approximately medium Reynolds Number by hot wire in order to investigate the scaling properties of the overlapped turbulent spectrum among energy-containing area, inertial subrange and dissipation range based on FFT analysis. The experiment indicates that the high Reynolds flow reported before is not indispensable to produce −1 scaling. So far as the measured position is provided with much higher spatial resolution and enough closing to the wall, −1 scaling is determinate to exist when approaching medium Reynolds. The scaling ranges are supposed to begin at inner scale and end in outer scale, which reveals the local similarity of the energy spectrum over the energy-containing eddies near the wall. In the logarithmic area (y ⁺ > 130), −5/3 scaling occurs in the energy spectrum, while moving away from the wall with Reynolds numbers increasing, the inertial subrange extends to the lower wavenumbers. On the condition k ₁ η ≫ 0.1, the curves of the turbulence spectrum in the logarithmic layer are superposed, which expresses the similarity of turbulence energy distributed in Komogorov scaling area and exhibits local isotropy characteristics by virtue of the viscous dissipation. Supported by the National Natural Science Foundation of China (Grant Nos. 10832001 and 10872145), the Program for New Century Excellent Talents in Universities of Education Ministry of China, and the Plan of Tianjin Science and Technology Development (Grant No. 06TXTJJC13800)     

Branched immersions and braids

Branch points of a real 2-surface Σ in a 4-manifold M generalize branch points of complex curves in complex surfaces: for example, they can occur as singularities of minimal surfaces. We investigate such a branch point p when Σ is topologically embedded. It defines a link L(p), the components of which are closed braids with the same axis up to orientation. If Σ is closed without boundary, the contribution of p to the degree of the normal bundle of Σ in M can be computed on the link L(p), in terms of the algebraic crossing numbers of its components and of their linking numbers with one another.      

Natural frequencies of submerged piezoceramic hollow spheres

An exact 3D analysis of free vibration of a piezoceramic hollow sphere submerged in a compressible fluid is presented in this paper. A separation method is adopted to simplify the basic equations for spherically isotropic piezoelasticity. It is shown that there are two independent classes of vibration. The first one is independent of the fluid medium as well as the electric field, while the second is associated with both the fluid parameter and the piezoelectric effect. Exact frequency equations are derived and numerical results are obtained. The project supported by the National Natural Science Foundation of China (No. 19872060)     

横观各向同性半无限空间表面典型荷载作用下的地基附加应力系数

在胡海昌和Lekhnitskii解的基础上,求得了地基表面作用竖直载荷时的附加应力系数的统一表达式,它可同时适用于各向同性和横观各向同性地基材料。详细讨论了5种典型载荷工况:圆形均布荷载、矩形均布荷载、矩形三角形分布荷载、均布线性和条形荷载。解的最终结果可由初等函数表示。文中同时也通过数值例子图示了材料各向异性对附加应力系数的影响。