Reissner板中的夹杂和缺陷问题研究

基于保角变换技术和Faber级数展开，研究了含任意形状夹杂或缺陷的无限大Reissner板弯曲问题．将变换域中单位圆内、外解析函数分别展开成Faber级数，并将波动函数展开成第一类和第二类修正的n阶Bessel函数；利用边界位移、剪力和弯矩连续性条件得到问题的高阶线性方程组．以含椭圆形夹杂和缺陷的无限大Reissner板柱面弯曲为例，进一步给出了数值算例和理论分析．结果表明，对于软夹杂，板内力矩随夹杂与板厚尺寸比a/h变化非常敏感；在含硬夹杂条件下，板内力矩随夹杂尺寸变化相对不敏感．

Research on Reissner Plate With an Inclusion or Flaw

The bending problems for the Reissner plate with arbitrarily shaped inclusion or flaw were solved with the conformal transformation method and Faber series expanding. The analytical functions were expanded with Faber series, and the wave functions were expressed by n-order first-kind and second-kind modified Bessel functions in/out the unit circle in the transform domain. The linear equations were obtained under the continuous displacement, shear force and bending moment conditions along the interface of the unit circle. The numerical examples and the theoretical analysis were presented for the Reissner plate with an elliptic inclusion or flaw under cylindrical bending. It is concluded that, the inner torques in the plate are sensitive to the ratio a/h for the soft inclusion, and are insensitive for the stiff one.