New Method for Geometric Nonlinear Analysis of Large Displacement Drill Strings

TAN Mei-lan; WANG Xin-wei

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TAN Mei-lan, WANG Xin-wei. New Method for Geometric Nonlinear Analysis of Large Displacement Drill Strings[J]. Applied Mathematics and Mechanics, 2005, 26(7): 847-853.

Citation:

TAN Mei-lan, WANG Xin-wei. New Method for Geometric Nonlinear Analysis of Large Displacement Drill Strings[J]. Applied Mathematics and Mechanics, 2005, 26(7): 847-853.

Citation:

TAN Mei-lan, WANG Xin-wei. New Method for Geometric Nonlinear Analysis of Large Displacement Drill Strings[J]. Applied Mathematics and Mechanics, 2005, 26(7): 847-853.

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New Method for Geometric Nonlinear Analysis of Large Displacement Drill Strings

TAN Mei-lan^1,2,
WANG Xin-wei²

1.
Faculty of Science, Jiangsu University, Zhenjiang 212013, P. R. China;

Received Date: 2003-10-09
Rev Recd Date: 2005-03-08
Publish Date: 2005-07-15

Abstract

Abstract

Based on the actual measured well depth, azimuth and oblique angles, a novel interpolation method to obtain the well axis is developed. The initial stress of drill string at the reference state being consistent with well axis can be obtained from the curvatures and the tortuosity of well axis. By using the principle of virtual work, formula to compute the equivalent load vector of the initial stress was derived. In the derivation, natural (curvilinear) coordinate system was adopted since both the curvature and the tortuosity were generally not zero. A set of displacement functions fully reflecting the rigid body modes was used. Some basic concepts in the finite element analysis of drill string have been clarified. It is hoped that the proposed method would offer a theoretical basis for handling the geometry nonlinear problem of the drill string in a 3-D large displacement wellbore.
- finite element,
- geometric nonlinearity,
- numerical simulation,
- drill string

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References(13)

References

[1]	刘延强，吕英民.环空钻柱结构三维非线性分析[J].应用数学和力学，1994，15(3):259—272.
[2]	于永南，帅健，吕英民,等.下部钻具组合的大变形分析——有限元动坐标迭代法的应用[J].石油大学学报，1993,17(1)：36—40.
[3]	刘延强，吕英民，于永南.环空大挠度钻柱力学分析的动坐标迭代法及其简化应用[J].计算结构力学及其应用，1998，19(1)：110—113.
[4]	Argyris J H.An excursion into large rotations[J].Computer Methods in Applied Mechanics and Engineering,1982,32(2/3):85—155. doi: 10.1016/0045-7825(82)90069-X
[5]	谈梅兰，王鑫伟.梁的三维空间大转动的有效处理方法[J].南京航空航天大学学报，2004,36(6):584—588.
[6]	吕英民.有限元法在钻柱力学中的应用——井眼轨迹控制理论与实践[M].山东：石油大学出版社，1996，8—12.
[7]	刘延强，蔡强康，吕英民. 三维井眼轴线的数值模拟计算[J].石油大学学报，1990，14(3):45—54.
[8]	谈梅兰，王鑫伟. 一种有效的分析任意空间形状曲杆单元的位移函数[J].工程力学，2004，21(3):134—137.
[9]	苏步青，胡和生，沈纯理,等.微分几何[M].北京：人民教育出版社，1979,6—7.
[10]	刘正兴，孙雁，王国庆.计算固体力学[M].上海：上海交通大学出版社，2000.
[11]	Love A E H.A Treatise on the Mathematical Theory of Elasticity[M].4th ed.New York: Dover Publications, 1927.
[12]	Yang T Y.Finite Element Structural Analysis[M].New Jersey:Prentice-Hall, 1986, 247—249.
[13]	Cook R D.Concepts and Applications of Finite Element Analysis[M].New York: John Wiley & Sons,1981，353—356.