莫尔应变圆极点法及应变极点特性研究

Study on the Pole Point Method of Mohr Strain Circle and the Characteristics of Strain Pole Point

极点是根据单元体的应变状态在莫尔应变圆上做出的一个特殊点,通过极点可以获得任意平面的应变状态。为确定莫尔应变圆上的极点,提出了2种方法——平行线法和法线法。采用反证法分别验证了平行线法和法线法确定的应变极点的唯一性,采用几何作图法分别验证了平行线法和法线法确定的应变极点的可靠性。研究表明:2种方法确定的应变极点位于莫尔应变圆的同一条直径上;应力极点与应变极点位于莫尔应力圆与应变圆组成的同心圆的半径上。莫尔应变圆极点法具有简便、准确的优点,避免了复杂的公式计算,是求解岩土工程中的稳定和变形问题及确定单元体复杂应变状态的优选方法。

The pole point on Mohr circle of strain is a point so special that it can help to readily find strains on any specified plane by using diagram instead of complicated computation. In this paper,two methods are put forward to determine the pole point on the Mohr circle of strain,i. e. the parallel line method and the normal line method. On the basis of contradiction method,the uniqueness of strain pole point is proved by parallel line method and normal line method; on the basis of geometric graphical method,the reliability of determining strain pole point by parallel line method and normal line method is verified. Research shows that the two strain pole points determined by the two methods are on a diameter line of the Mohr strain circle. When certain proportional relation is given,the corresponding stress pole point and the strain pole point are on the radius line of the concentric circle consisting of the Mohr stress circle and Mohr strain circle. The strain pole point method is a preferred solution to determine complex strain state of the strain element and the deformations in geotechnical fields.