含轴对称抛物线曲裂纹平面弹性问题的解析解

研究含轴对称抛物线曲裂纹平面弹性问题.采用了传统的复变函数保角映射法,给出了一个新的保角变换公式,从而将抛物线曲裂纹外的区域映射到一个复平面的单位圆内.得到了含轴对称抛物线曲裂纹平面弹性问题的曲裂纹尖端Ⅰ型应力强度因子的解析表达式.本解在特殊极限条件下可解析地退化到穿透型直线裂纹的经典解.参数分析表明轴对称抛物线曲裂纹尖端的应力强度因子与抛物线曲裂纹的尺寸和形状有关.

An Analytical Solution for the Elastic Plane Problem with a Symmetric Parabolic Crack

The problem of an elastic plane having symmetric parabolic crack is discussed. Classical complex variable method is followed, but a new conformal mapping formula is proposed so that the exterior part of the parabolic crack is mapped into a unit circle. An analytical solution for the mode I stress intensity factor at the crack tip of a symmetric parabolic crack is thus obtained. This solution analytically reduces to the classical solution for the line crack in a special case. It is found that the size and the shape of the parabolic crack affect the mode I stress intensity factor at the crack tips.