THE EVALUATION OF STRESS INTENSITY FACTORS OF PLANE CRACK FOR ORTHOTROPIC PLATE WITH EQUAL PARAMETER BY F2LFEM

In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method (F2LFEM). The general solution of an orthotropic crack problem is obtained by assimilating the problem with isotropic crack problem, and is employed as the global interpolation function in F2LFEM. In the neighborhood of crack tip of the crack plate, the fractal geometry concept is introduced to achieve the similar meshes having similarity ratio less than one and generate an infinitesimal mesh so that the relationship between the stiffness matrices of two adjacent layers is equal. A large number of degrees of freedom around the crack tip are transformed to a small set of generalized coordinates. Numerical examples show that this method is efficient and accurate in evaluating the stress intensity factor (SIF).     

Diffraction of stress waves by a free or reinforced hole in an orthotropic plate

Photoelastic plates made of an orthotropic material are used to model the dynamic stress state near free and reinforced circular holes under blast loading. The diffraction of stress waves by holes in a thin-walled plate is studied. Experimental data are used to analyze the dynamic stress concentration in a plate with a hole in which quasilongitudinal and quasitransverse waves propagate __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 73–78, July 2007.     

SH波在正交各向异性功能梯度无限长条中心裂缝处的散射

研究了正交各向异性功能梯度材料无限长条中心裂缝对SH波的散射问题,为方便起见,材料两个方向的剪切模量和密度假定为指数模型.通过Fourier积分变换,将问题转化为对偶积分方程的求解.然后,用Cop-son方法求解对偶积分方程,定义了标准动应力强度因子,通过数值算例,讨论了在SH波作用下,裂缝尖端的标准动应力强度因子与入射波的频率、材料参数之间的关系.     

Isotropic/orthotropic two-layered strips containing cracks terminating at and going through an interface

Crack problems for isotropic/orthotropic two-layered strips have been investigated. A system of two singular integral equations can be derived by using Fourier integral transformation and boundary conditions of crack problems. After stress singularities at crack tips or other special points are determined for internal and edge cracks, and for cracks terminating at and going through the interface, the system of singular integral equations is solved numerically by Gauss-Jacobi or Gauss-Chebyshev integration formulas for stress intensity factors at the tips and other singular points of cracks. Finally, possible crack growth behavior for cracks approaching and going through the interface is discussed.     

Propagation of SH‐wave in an initially stressed orthotropic medium sandwiched by a homogeneous and an inhomogeneous semi‐infinite media

The paper presents a study of propagation of shear wave (SH‐wave) in an orthotropic elastic medium under initial stress sandwiched by a homogeneous semi‐infinite medium and an inhomogeneous half‐space. The technique of separation of variables has been adopted to get the analytical solutions for the dispersion relation in a closed form. The propagation of SH‐waves is influenced by inhomogeneity parameters and initial stress parameter. Velocities of SH‐waves are calculated numerically for different cases. As a special case when the intermediate layer and half‐space are homogeneous, computed frequency equation coincides with general equation of Love wave. To study the effect of inhomogeneity parameters and initial stress parameter, we have plotted the velocity of SH‐wave in several figures and observed that the velocity of wave decreases with the increases of non‐dimensional wave number. It can be found that the phase velocity decreases with the increase of inhomogeneity parameters. We observed that the velocity of SH‐wave decreases with the increases of initial stress parameter in both homogeneous and inhomogeneous media. GUI has been developed by using MATLAB to generalize the effect of the parameters discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

The vibration and stability of non-homogeneous orthotropic conical shells with clamped edges subjected to uniform external pressures

In this paper an analytical procedure is given to study the free vibration and stability characteristics of homogeneous and non-homogeneous orthotropic truncated and complete conical shells with clamped edges under uniform external pressures. The non-homogeneous orthotropic material properties of conical shells vary continuously in the thickness direction. The governing equations according to the Donnell’s theory are solved by Galerkin’s method and critical hydrostatic and lateral pressures and fundamental natural frequencies have been found analytically. The appropriate formulas for homogeneous orthotropic and isotropic conical shells and for cylindrical shells made of homogeneous and non-homogeneous, orthotropic and isotropic materials are found as a special case. Several examples are presented to show the accuracy and efficiency of the formulation. The closed-form solutions are verified by accurate different solutions. Finally, the influences of the non-homogeneity, orthotropy and the variations of conical shells characteristics on the critical lateral and hydrostatic pressures and natural frequencies are investigated, when Young’s moduli and density vary together and separately. The results obtained for homogeneous cases are compared with their counterparts in the literature.     

均布载荷作用下正交各向异性一端固支一端简支梁的解析解

构造了一个应力函数，用Ariy应力函数逆解法给出了受均布载荷作用的正交各向异性矩形梁在一端固支一端简支条件下平面应力问题的解析解．采用的2种不同固支边界条件与Timoshenko and Goodier在1970年中所采用的方法相同，并给出了数值算例．     

高层束筒建筑板块法理论

本文给出了正交异性板在多种平面应力边界条件下的应力分布解析表达式，由此提出了多筒高层框筒（或剪力墙筒体）内力与位移计算的正变异性板板块法理论．该方法是基于力法体系及形变协调条件的半解析法，可方便地应用于多筒筒体或多室梯形箱梁等折板结构分析。     

Determination of stresses in slightly orthotropic plates using off-axis horizontally polarized ultrasonic shear waves

Many structural materials display a slight orthotropy when they are rolled into plate form. A theory is developed for propagation of horizontally polarized ultrasonic shear waves in the planes of (orthotropic) material symmetry of these plates. The waves propagate at an angle θ to the plate normal. If E represents a measure of the shear stress field, then pure-mode waves can be propagated if both cos² θ and sin² θ E; the polarization directions are the material symmetry axes.

The theory can be applied to ultrasonic stress measurements. The (normalized) velocity difference (acoustic birefringence) between two pure-mode SH-waves propagating in orthogonal material symmetry planes is related to stresses in the plate, and to the (initial) birefringence in the unstressed state. By making measurements of birefringence at two or more values of θ, the dependence upon the initial birefringence can be removed and information about the stresses obtained.     

Natural Frequency for Rectangular Orthotropic Corrugated-Core Sandwich Plates with All Edges Simply-Supported

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