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Special solutions for the ring circular domain with crack surfaces acted on uniform compressive force, linear compressive force and linear shearing force are deduced in polar coordinate employed the eigenfunction expansion technique in the Hamiltonian system of elastic mechanics. Combined with the general solution for the above problems, the analytical solutions for crack tip fields with surfaces acted on the above three kinds of loads are obtained. These solutions offer theoretical basis to construct analytical elements for plastic analysis of crack.

从弹性力学哈密顿体系理论出发,利用平面弹性力学极坐标系下的本征向量展开求解,推导了环形圆形域裂纹边作用有均布压力、线性压力和均布剪切力情况下的特解,从而得到了裂纹表面作用有以上三种荷载情况下的裂纹尖端场的解析解,为进一步构造进行弹塑性裂纹分析的奇异解析元奠定了理论基础。

It includes hardware equipments and foundational theory of the image digitization. This paper expatiates on some digital image processing technologies that the inspecting system may apply to the research and analysis of the collected glass-crack image. Using neighborhood average method and median filter retrains the image noises and make the image edge smooth. Then protract the histogram of the gray image, get the threshold of this image, utilize the threshold method and gray-level slice method to get a binary image, and detect the image edge. Finally calculate the area and perimeter of the glass-crack image, and use the circularity to judge whether this image is a glass-crack image.

本文重点阐述了研究和开发这套玻璃瓶裂纹检测系统所应用到的一些数字图像处理技术,并应用这些技术和方法对采集的裂纹图像进行了处理和分析:应用邻域平均法和中值滤波法来抑制图像的噪声,使图像的边缘平滑;然后绘制出处理过图像的灰度直方图,得到该幅裂纹图像的阈值,利用阈值法和灰度级切片法对裂纹图像进行二值化处理,得到其二值图像,并对图像进行了边缘检测;最后计算出裂纹图像的面积和周长,利用圆形度指标来判断该图像是否为裂纹图像。

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