Abstract: The basic theory of a previous researcher was analyzed by using the reduction to absurdity.The problems existing in his deduction were discussed.It is proved that there is no contradiction between biaxial stress ellipse theory and practical loading condition.The monotone property of multivariate function proved that the maximum stress strength point exists on the inner surface of casing under the triaxial stress conditions.The formula for calculating the axial stress of casing was discussed with theoretic deduction and calculation methods.The calculation case shows that the result of collapse strength calculated by using the triaxial stress circle theory is bigger than that by other theories.

Key words: casing strength, biaxial stress ellipse theory, casing design, axial stress, calculation formula

摘要： 采用反证法探讨了前人在基础理论的推理过程中存在的问题,证明双向应力椭圆理论与实际载荷条件并不矛盾。应用多元函数单调性理论,证明了在三轴应力条件下管体中最大应力强度值出现在套管内壁。采用理论推导和计算方法,对套管轴向应力计算公式进行了讨论。通过实例计算,对比分析了用“三向应力圆”理论与其他几种理论计算的抗挤强度值。结果表明,应用“三向应力圆”理论计算的值偏大。

关键词: 套管强度, 双向应力椭圆理论, 套管设计, 轴向力, 计算公式