正交各向异性板Ⅲ型裂纹问题的William′s一般解

William′s general solution to mode Ⅲ two-dimensional crack problem of orthotropic media

引入参数β=μx/μy,将正交各向异性板反平面裂纹问题的基本边值问题转换为正交各向同性的形式,反平面裂纹问题的位移和应力在正交各向同性和正交各向异性这两种情况之间的比拟关系非常简单,使问题的求解更为方便.为了说明这个比拟方法,分别求导了含有内部裂纹和边缘裂纹的正交各向异性板Ⅲ型二维裂纹问题的William′s一般解.这些William′s一般解对于用FFEM和其他数值方法来求解正交各向异性板反平面裂纹问题是一个非常重要的基础.研究结果表明这种比拟变换方法能有效地简化正交各向异性板Ⅲ型裂纹问题的求解.

The basic equations of antiplane crack problem for orthotropic media were transformed by introducing the parameter in terms of those of isotropic media. The analogy relationship between the displacements and stresses of an anti-plane crack in an isotropic and an orthotropic plate is very simple so that the inverse transform is convenient. For explaining this analogy method, the William＇s general solutions to mode Ⅲ two-dimensional crack problem of orthotropic plates with internal and edge cracks are derived, respectively. This analogy method is efficient for solving anti-plane crack problems of orthotropic plates.