巴西劈裂试验应力场解析解应力函数解法

巴西圆盘试验是国际岩石力学学会推荐的用于测量岩石抗拉强度的间接实验，其理论基础是圆盘在荷载作用下应力场的分布。本文以平面应力状态为基础，根据弹性理论中的Airy应力函数和线弹性叠加原理，采用与Н. И. Мусхелишьили所用的复变函数方法完全不同的方法，给出了巴西圆盘内部任意一点应力的直角坐标形式的解析表达式。将得到的应力场解析解和Н.И. Мусхелишьили 采用复变函数方法给出的经典解对比发现，两者完全吻合一致，从而表明本文所采用的方法是合理正确的。

AIRY STRESS FUNCTION METHOD FOR ANALYTIC SOLUTION OF STRESS FIELD DURING BRAZILIAN DISC TEST

Brazilian disc test is an indirect experiment, proposed by International Society for Rock Mechanics, to determine the tensile strength of rock materials. The theoretical foundation is the distribution of stress field in the disc under the concentration loads applied. In this study, the analytic stress solution in the form of Cartesian Coordinates of any point in the disc is given with a new method. It is completely different with the complex function method according to the Airy stress function and the superposition principle of linear elasticity. Comparing the analytic stress solution obtained here and the typical solution given by Н. И. Мусхелишьили, it is found that they are consistent with each other completely. Accordingly, it is proved that the procedure and the method adopted here are both reasonable and appropriate.