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中文摘要：
在推导非均匀地应力下套管抗挤强度的解析解时，国内外许多学者采用将其分解为均匀地应力和偏差地应力两个子问题求解的方法，使问题复杂化；又因为在推导套管载荷的解析解过程中省略了小量值，还影响到求解的精度。为此。以弹性力学为基础，推导出了计算套管-水泥环-地层系统应力的线性方程组，并利用matlab7．0编制了相应的计算机程序求解。该方法推导过程简单、求解精度高，所得结果与有限元结果相比，相对误差小于0．3％。实例分析结果表明：在非均匀地应力下套管径向压力的最大值方向指向原地应力场中最小主应力，而水泥环径向压力的最大值方向指向原地应力场中最大主应力。
英文摘要：
In the process of developing analytical solutions to casing collapse strength in condition of heterogeneous in situ stress, a lot of researchers divide it into two problems, a uniform in-situ stress and a deviation in-situ stress, which complicates the problem and reduces accuracy due to ignorance of small values. New linear equations were generated based on the elasticity theory. Matlab 7.0 was used to solve the equations. The comparison with finite element results indicates the relative error is less than 0.3%. The numerical example indicates the maximum compression stress of casing directs to the formation＇s minimum principal stress, the maximum compression stress of cement directs the formation＇s maximum principal stress.
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