The 3-D stress intensity factor for a half plane crack in a transversely isotropic solid due to the motion of loads on the crack faces

Three-dimensional analysis of a half plane crack in a transversely isotropic solid is performed. The crack is subjected to a pair of normal point loads moving in a direction perpendicular to the crack edge on its faces. Transform methods are used to reduce the boundary value problem to a single integral equation that can be solved by the Wiener-Hopf technique. The Cagniard-de Hoop method is employed to invert the transforms. An exact expression is derived for the mode I stress intensity factor as a function of time and position along the crack edge. Some features of the solution are discussed through numerical results. The project supported by the Guangdong Provincial Natural Science Foundation and the Science Foundation of Shantou University     

Penny-shaped and half-plane cracks in a transversely isotropic piezoelectric solid under arbitrary loading

Summary The problem of a penny-shaped crack in a transversely isotropic piezoelectric material loaded by both normal and tangential tractions and by electric charges is analyzed. Closed-form solutions are obtained for the full electroelastic fields as well as for the stress and electric displacement intensity factors. Solutions are also obtained for the (non-trivial) limiting case of a half-plane crack. The results are illustrated on the example of piezoceramics PZT-6B. Received 12 July 1999; accepted for publication 20 July 1999     

一种用于层状结构模型的先进计算方法

提出一种针对层状结构模型的先进计算方法。研究的层状结构通常为水平层状板或者层状半空间,结构由横观各向同性（TI）材料组成,材料对称轴指向分层方向。本文方法可以考虑材料的多场耦合特性,即热弹性、多孔弹性和磁电弹性耦合。基于最近提出的傅立叶-贝塞尔级数（FBS）向量函数系和双变量/位置（DVP）方法,建立了本文的先进计算方法。DVP能够无条件稳定地将层矩阵从一层传播到下一层。FBS向量函数系具有以下特点,（1）反映了具有明确类型的广义变形/波,（2）将展开系数预先计算为Love数,然后将其用于涉及问题的模拟。层状地球中的断层（或位错）作用、土-结构相互作用以及近地表地球剖面中的瞬态波等三个典型算例,证明了提出方法的准确性和有效性。     

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)     

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

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｓｏｉｌｍｅｃｈａｎｉｃｓ,ｔｈｅｐｒｏｂｌｅｍｓｄｅａｌｉｎｇｗｉｔｈｓｔｒｅｓｓｉｎｆｏｕｎｄａｔｉｏｎｓａｒｅｕｓｕａｌｌｙｒｅｆｅｒｒｅｄａｓｔｈｅＢｏｕｓｓｉｎｅｓｑｓｏｌｕｔｉｏｎｓａｎｄｔｈｅＣｅｒｒｕｔｉｏｎｅｓ (Ｌｏｖｅ[1 ] ;Ｌｕｒｅ[2 ] ) .Ｆｕｒｔｈｅｒｉｎｖｅｓｔｉｇａｔｉｏｎ (Ｂａｒｄｅｗ[3 ] ;Ｇｉｂｓｏｎ[4 ] )ｔｏｏｋｔｈｅｆｏｕｎｄａｔｉｏｎａｓａｐｐｒｏｘｉｍａｔｉｏｎｏｆｔｒａｎｓｖｅｒｓｅｌｙｉｓｏｔｒｏｐｉｃｈａｌｆ＿ｓｐａｃｅ .Ｍ…     

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。     

A Natural Generalization of Hypoelasticity and Eulerian Rate Type Formulation of Hyperelasticity

According to the classical hypoelasticity theory, the hypoelasticity tensor, i.e. the fourth order Eulerian constitutive tensor, characterizing the linear relationship between the stretching and an objective stress rate, is dependent on the current stress and must be isotropic. Although the classical hypoelasticity in this sense includes as a particular case the isotropic elasticity, it fails to incorporate any given type of anisotropic elasticity. This implies that one can formulate the isotropic elasticity as an integrable-exactly classical hypoelastic relation, whereas one can in no way do the same for any given type of anisotropic elasticity. A generalization of classical theory is available, which assumes that the material time derivative of the rotated stress is dependent on the rotated Cauchy stress, the rotated stretching and a Lagrangean spin, linear and of the first degree in the latter two. As compared with the original idea of classical hypoelasticity, perhaps the just-mentioned generalization might be somewhat drastic. In this article, we show that, merely replacing the isotropy property of the aforementioned stress-dependent hypoelasticity tensor with the invariance property of the latter under an R-rotating material symmetry group R⋆ G ₀, one may establish a natural generalization of classical theory, which includes all of elasticity. Here R is the rotation tensor in the polar decomposition of the deformation gradient and G ₀ any given initial material symmetry group. In particular, the classical case is recovered whenever the material symmetry is assumed to be isotropic. With the new generalization it is demonstrated that any two non-integrable hypoelastic relations based on any two objective stress rates predict quite different path-dependent responses in nature and hence can in no sense be equivalent. Thus, the non-integrable hypoelastic relations based on any given objective stress rate constitute an independent constitutive class in its own right which is disjoint with and hence distinguishes itself from any class based on another objective stress rate. Only for elasticity, equivalent hypoelastic formulations based on different stress rates may be established. Moreover, universal integrability conditions are derived for all kinds of objective corotational stress rates and for all types of material symmetry. Explicit, simple, integrable-exactly hypoelastic relations based on the newly discovered logarithmic stress rate are presented to characterize hyperelasticity with any given type of material symmetry. It is shown that, to achieve the latter goal, the logarithmic stress rate is the only choice among all infinitely many objective corotational stress rates. This revised version was published online in August 2006 with corrections to the Cover Date.     

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).     

近零膨胀Zr0.5Hf0.5V1.4P0.6O7材料的制备及其性能研究

采用传统的固相法合成了近零膨胀氧化物功能陶瓷材料Zr_0.5Hf_0.5V_1.4P_0.6O₇,用X射线衍射(XRD)、Raman光谱和热膨胀法对Zr_0.5Hf_0.5V_1.4P_0.6O₇的热膨胀系数、各向同性和相变进行了测试,通过Hf⁴⁺/P⁵⁺共掺杂使得材料具有较低的热膨胀系数,研究发现合成的Zr_0.5Hf_0.5V_1.4P_0.6O₇具有Pa3立方相结构,从334 K附近到673 K较宽的温度范围内的线性热膨胀系数为-1.56×10^-6 K^-1,表现出稳定的近零热膨胀特性。由于固溶体内部微结构的影响造成膨胀仪实验结果与变温X射线衍射结果存在一定的差距。Zr_0.5Hf_0.5V_1.4P_0.6O₇具有的近零膨胀特性为通过负热膨胀材料合成膨胀系数可控的材料提供了基础。