论文标题
环形和圆形的刚性夹杂物种植成一分钱的裂纹和三角矩阵的分解
Annular and circular rigid inclusions planted into a penny-shaped crack and factorization of triangular matrices
论文作者
论文摘要
当将任意轮廓包含在环形形状（模型1）或圆盘形（模型2）刚性（模型2）固定二个轴形裂缝的两个轴对称问题中。这些问题由与Weber-sonin内核的整体方程组成。通过Mellin卷积定理，与模型1和2相关的积分方程减少到矢量riemann-Hilbert的问题以及3x3和2x2和2x2三角矩阵系数，其条目由Meromororphic和Infinite指数指数函数组成。得出了分解的规范矩阵，并计算了部分指标。获得正常应力，应力强度因子和正常位移的精确表示公式，并报告了数值测试的结果。
Analytical solutions to two axisymmetric problems of a penny-shaped crack when an annulus-shaped (model 1) or a disc-shaped (model 2) rigid inclusion of arbitrary profile are embedded into the crack are derived. The problems are governed by integral equations with the Weber--Sonin kernel on two segments. By the Mellin convolution theorem the integral equations associated with the models 1 and 2 reduce to vector Riemann-Hilbert problems with and 3x3 and 2x2 triangular matrix coefficients whose entries consist of meromorphic and of infinite indices exponential functions. Canonical matrices of factorization are derived and the partial indices are computed. Exact representation formulas for the normal stress, the stress intensity factor, and the normal displacement are obtained and the results of numerical tests are reported.
