ANALYSIS ON ACOUSTICAL SCATTERING BY A CRACKED ELASTIC STRUCTURE

The acoustical scattering by a cracked elastic structure is studied. The mixed method of boundary element and fractal finite element is adopted to solve the cracked structure-acoustic coupling problem. The fractal two-level finite element method is employed for the cracked structure, which can reduce the degree of freedoms (DOFs) greatly, and the boundary element method is used for the exterior acoustic field which can automatically satisfy Sommerfeld‘s radiation condition. Numerical examples show that the resonance frequency is lower with the crack‘s depth increase, and that the effect on the acoustical field by the crack is particularly pronounced in the vicinity of the crack tip. This mixed method of boundary element and finite element is effective in solving the scattering problem by a cracked structure.     

Ⅱ-Ⅲ混合型裂纹相变增韧分析

本文采用压力敏感准则和松函数法对相变增韧陶瓷Ⅱ-Ⅲ混合型裂纹的增韧效应进行了理论预测。分别给出了静止裂纹和定常扩展裂纹相变塑性屏蔽的理论表达式。结果表明：相变对静止裂纹有甚微的负屏蔽效应，并随KⅢ/KⅡ的比值而波动；相变对定常扩展裂纹的增韧结果除与材料弹性模量、相变尾区高度和相变体积分数有关外，还与KⅢ/KⅡ的比值有关。     

Variation of the stress intensity factor along the front of a 3-D rectangular crack subjected to mixed-mode load

Summary  The singular integral equation method is applied to the calculation of the stress intensity factor at the front of a rectangular crack subjected to mixed-mode load. The stress field induced by a body force doublet is used as a fundamental solution. The problem is formulated as a system of integral equations with r ⁻³-singularities. In solving the integral equations, unknown functions of body-force densities are approximated by the product of polynomial and fundamental densities. The fundamental densities are chosen to express two-dimensional cracks in an infinite body for the limiting cases of the aspect ratio of the rectangle. The present method yields rapidly converging numerical results and satisfies boundary conditions all over the crack boundary. A smooth distribution of the stress intensity factor along the crack front is presented for various crack shapes and different Poisson's ratio. Received 5 March 2002; accepted for publication 2 July 2002     

ELECTROELASTIC FIELD FOR AN IMPERMEABLE ANTI-PLANE SHEAR CRACK IN A PIEZOELECTRIC CERAMICS PLATE

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陶瓷阻力曲线测定的新方法——断裂栅法

将零厚度单向试件栅刻蚀工艺应用于晶须增韧氮化硅陶瓷基复合材料表面，通过记录试件所在桥路的输出电压值，可得到随载荷不断增大裂纹逐渐向前扩展过程中每一时刻的裂尖位置和裂纹长度，从而得到该种材料的阻力曲线。     

Stage-I fatigue crack studies in order to validate the dislocation-free zone model of fracture for bulk materials

Stage-I fatigue cracks are commonly described by the model of Bilby, Cottrell and Swinden (BCS model). However, since several experimental investigations have shown a dislocation-free zone (DFZ) in front of crack-tips, it is necessary to validate the new DFZ model and to examine the deviations to the BCS model. Therefore, the dislocation density distribution is derived from height profiles of slip lines in front of stage-I fatigue cracks in CMSX4® single crystals measured by contact-mode atomic force microscopy. This is possible, because the cracks are initiated at notches milled by focused ion beam technique directly on slip planes with a high Schmid factor. Consequently, the directions of the Burgers vectors are well known; it is possible to calculate the dislocation density distributions from the height profiles. The measured distributions are compared to the calculated distribution function of the DFZ model proposed by Chang et al. The additionally measured microscopic friction stress of the dislocations is then used to calculate the influence of grain boundaries on the dislocation density distribution in front of stage-I cracks. The calculation is done by the extended DFZ model of Shiue et al. and compared with the measured distribution function in polycrystalline specimens. Finally, the crack-tip sliding displacement as a measure for the crack propagation rate is compared for the DFZ model and the BCS model with the experimentally revealed values. The important result: the often used BCS model does not reflect the experimental measurements. On the contrary, the DFZ model reflects the measurements at stage-I cracks qualitatively and quantitatively.     

A blow‐up criterion to the 2D full compressible magnetohydrodynamic equations

We establish a new regularity criterion for the 2D full compressible magnetohydrodynamic system in a bounded domain. Copyright © 2014 John Wiley & Sons, Ltd.     

An efficient meshfree point collocation moving least squares method to solve the interface problems with nonhomogeneous jump conditions

We are going to study a simple and effective method for the numerical solution of the closed interface boundary value problem with both discontinuities in the solution and its derivatives. It uses a strong‐form meshfree method based on the moving least squares (MLS) approximation. In this method, for the solution of elliptic equation, the second‐order derivatives of the shape functions are needed in constructing the global stiffness matrix. It is well‐known that the calculation of full derivatives of the MLS approximation, especially in high dimensions, is quite costly. In the current work, we apply the diffuse derivatives using an efficient technique. In this technique, we calculate the higher‐order derivatives using the approximation of lower‐order derivatives, instead of calculating directly derivatives. This technique can improve the accuracy of meshfree point collocation method for interface problems with nonhomogeneous jump conditions and can efficiently estimate diffuse derivatives of second‐ and higher‐orders using only linear basis functions. To introduce the appropriate discontinuous shape functions in the vicinity of interface, we choose the visibility criterion method that modifies the support of weight function in MLS approximation and leads to an efficient computational procedure for the solution of closed interface problems. The proposed method is applied for elliptic and biharmonic interface problems. For the biharmonic equation, we use a mixed scheme, which replaces this equation by a coupled elliptic system. Also the application of the present method to elasticity equation with discontinuities in the coefficients across a closed interface has been provided. Representative numerical examples demonstrate the accuracy and robustness of the proposed methodology for the closed interface problems. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1031–1053, 2015     

Strong solutions to the equations of electrically conductive magnetic fluids

We study the equations of flow of an electrically conductive magnetic fluid, when the fluid is subjected to the action of an external applied magnetic field. The system is formed by the incompressible Navier–Stokes equations, the magnetization relaxation equation of Bloch type and the magnetic induction equation. The system takes into account the Kelvin and Lorentz force densities. We prove the local-in-time existence of the unique strong solution to the system equipped with initial and boundary conditions. We also establish a blow-up criterion for the local strong solution.     

A logarithmic regularity criterion for the 3D generalized MHD system

We prove a logarithmic regularity criterion for the 3D generalized magnetohydrodynamics (MHD) system with diffusion terms ?Δu and (?Δ)^βb, with . Copyright © 2015 John Wiley & Sons, Ltd.