New Method for Geometric Nonlinear Analysis of Large Displacement Drill Strings
-
摘要: 提出了基于实测的井深及相应的井斜角和方位角来获得确保井内钻柱参考构形长度不变的井眼轴线插值方法．当以空间大位移井的井眼轴线为钻柱的参考构形时，钻柱内的初始内力可以由井眼轴线的曲率和挠率确定．利用基于在空间自然坐标系下的包含所有单元刚体位移和常应变模式的位移函数，严格地按虚功原理推出了具有初始曲率和挠率的钻柱单元内由初始内力所引起的等效节点力计算公式，为大位移井钻柱的几何非线性处理提供了理论依据．澄清了钻柱有限元分析中的若干基本概念．为随后进行的以井眼轴线为参考构形的小变形分析，计算钻柱的自重和基于自然坐标系下的线性刚度矩阵及一致载荷列阵提供了保证．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.
-
Key words:
- finite element /
- geometric nonlinearity /
- numerical simulation /
- drill string
-
[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. -
计量
- 文章访问数: 2603
- HTML全文浏览量: 95
- PDF下载量: 586
- 被引次数: 0
下载:
渝公网安备50010802005915号