Green function and its application for a piezoelectric plate with various openings

Summary For a two-dimensional piezoelectric plate subjected to mechanical and electric load, a Green function satisfying traction free and exact electric boundary conditions along a hole is developed using Lekhnitskii's formalism and the technique of conformal mapping. The critical points for the mapping function used is investigated numerically, and the study indicates that the transformation of a polygonal hole in a piezoelectric plate into a unit circle is nonsingle-valued. A simple approach is presented to treat such a situation. Based on the Green function developed in this paper, a system of singular integral equations for the unknown dislocation defined on crack faces is presented to study the interaction between cracks and holes. Numerical results are presented to elucidate the effects of crack orientation on stress and electric displacement (SED) intensity factors and to illustrate the application of the proposed formulation. Received 4 June 1998, accepted for publication 15 July 1988     

Equivalence Theorems on the Propagation of Small-Amplitude Waves in Prestressed Linearly Elastic Materials with Internal Constraints

By extending the procedure of linearization for constrained elastic materials in the papers by Marlow and Chadwick et al., we set up a linearized theory of constrained materials with initial stress (not necessarily based on a nonlinear theory). The conditions of propagation are characterized for small-displacement waves that may be either of discontinuity type of any given order or, in the homogeneous case, plane progressive. We see that, just as in the unconstrained case, the laws of propagation of discontinuity waves are the same as those of progressive waves. Waves are classified as mixed, kinematic, or ghost. Then we prove that the analogues of Truesdell"s two equivalence theorems on wave propagation in finite elasticity hold for each type of wave. This revised version was published online in August 2006 with corrections to the Cover Date.     

Green's function for thermopiezoelectric plates with holes of various shapes

Summary Thermoelectroelastic problems for holes of various shapes embedded in an infinite matrix are considered in this paper. Based on Lekhnitskii's formalism, the technique of conformal mapping and the exact electric boundary conditions on the hole boundary, the thermoelectroelastic Green's function has been obtained analytically in terms of a complex potential. As an application of the proposed function, the problem of an infinite plate containing a crack and a hole is analysed. A system of singular integral equations for the unknown temperature discontinuity and the discontinuity of elastic displacement and electric potential (EDEP) defined on crack faces is developed and solved numerically. Numerical results for stress and electric displacement (SED) intensity factors of the crack-hole system are presented to illustrate the application of the proposed formulation. Received 7 October 1998; accepted for publication 26 January 1999     

Experimental caustics analysis in fracture mechanics of anisotropic materials

The originally developed reflection method of caustics is presented for application to cracks in mechanically anisotropic materials such as fiber-reinforced composites. The derived solutions for the combination of crack-opening modes I and II show that the size of the dark spot depends on the load intensity, whereas its shape depends strongly on the mechanical properties of the material, the orientation of the crack tip and the mixed-mode mixture. The evaluation of optical effects is possible using the diameter-measuring method or the advanced multipoint overdeterministic data reduction method. To find the exact position of caustics, the experimental images are analyzed by the simple boundary value method and a more sophisticated differential method, which is accomplished by shifting the real image onto the gradient image. The standard experimental testing procedure is performed for cracks oriented 0 deg, 45 deg and 90 deg to the material axes in carbon-fiber-reinforced polymer composites.     

双材料界面裂纹应力强度因子的边界元分析

采用双材料基本解建立边界元法基本方程,计算双材料界面裂纹尖端附近的应用力和位移场。不离散界面,并设置面力奇异四分之一点裂尖单元以提高计算精度。数值结果表明,本文的方法具有较高的精度和效率。     

The efect of the couple stress parameter and Prandtl number on the transient natural convection flow over a vertical cylinder

An analysis is performed to study transient free convective boundary layer flow of a couple stress fluid over a vertical cylinder, in the absence of body couples. The solution of the time-dependent non-linear and coupled governing equations is carried out with the aid of an unconditionally stable Crank–Nicolson type of numerical scheme. Numerical results for the steady-state velocity, temperature as well as the time histories of the skin-friction coefcient and Nusselt number are presented graphically and discussed. It is seen that for all flow variables as the couple stress control parameter, Co, is amplified, the time required for reaching the temporal maximum increases but the steady-state decreases.     

A rigid inclusion in an elastic space under the action of a uniform heat flow in the inclusion plane

A solution is presented for the three dimensional static thermoelastic problem of an absolutely rigid inclusion (anticrack) in the case when a uniform heat flow is directed along the inclusion plane. By using the potential method and the Fourier transform technique, the problem is reduced to a system of coupled two-dimensional singular integral equations for the shear stress jumps across the inclusion. As an illustration, a typical application to the circular anticrack is presented. Explicit expressions for the thermal stresses in the inclusion plane are obtained and discussed from the point of view of material failure.     

Triaxial stress state of cylindrical openings for rocks modeled by elastoplasticity and strength criterion

An analytical solution for calculating the triaxial stress state around a cylindrical opening in an elastoplastic cohesive medium is developed. Magnitude of the slip zones around a cylindrical opening in crack-weakened rock masses is considered by modifying the existing strength criterion for rocks of different types. The disturbance coefficient, the geological strength index and the other strength parameters are also investigated.     

Methodology to assess integrity with application to collector copper lamellas

The performance of engineering components and structures is strongly influenced by the interaction between design, manufacture and materials. A methodology to assess the integrity of a circular collector is presented by investigating the failure of copper lamellas. The investigated circular collector, having 315 copper lamellas, is one of the main parts of an electric motor. The fracture of the copper lamellas was observed in normal operation. This unexpected fracture required an investigation of the fracture origin, in order to improve the initial design. The numerical results of the finite element analysis on the stress field in the copper lamellas for the operating regimes, and the stress concentration effects are shown. Failure assessment diagram, based on notch stress intensity factor, was considered in order to estimate if crack initiation can occur. Finally a study of crack propagation will present comparatively the numerical obtained crack path against the one observed in-service.     

Axial Couette flow of an Oldroyd-B fluid in an annulus

This paper establishes the velocity field and the adequate shear stress corresponding to the motion of an Oldroyd-B fluid between two infinite coaxial circular cylinders by means of finite Hankel transforms. The flow of the fluid is produced by the inner cylinder which applies a time-dependent longitudinal shear stress to the fluid. The exact analytical solutions, presented in series form in terms of Bessel functions, satisfy all imposed initial and boundary conditions. The general solutions can be easily specialized to give similar solutions for Maxwell, second grade and Newtonian fluids performing the same motion. Finally, some characteristics of the motion as well as the influence of the material parameters on the behavior of the fluid motion are graphically illustrated.