摘要
斜直井内计重柔性钻柱的非线性屈曲属于强非线性问题研究的范畴。鉴于Newton-Raphson法一般只对弱非线性有效,难以满足工程实际对计算精度及可靠性的要求,用圆柱坐标系表示的钻柱屈曲四阶非线性平衡微分方程可以用微分求积单元法直接进行数值求解,结合DQ单元,用弧长法构建了增量迭代法。用两个工程实例验证了方法的有效性。数值结果表明,DQ单元法克服了有限单元法在处理钻柱自重方面的困难,提高了解的精度。基于DQ单元的弧长迭代法,方法简单,易于实施,收敛性好,能准确地捕捉到螺旋屈曲的临界载荷。因此,可方便地用于求解斜直井内钻柱的非线性屈曲问题。
Nonlinear buckling of flexible drill strings with weight in slant wells belongs to a research category of strong nonlinear problems.Since the Newton-Raphson method is generally valid only for weakly nonlinear problems and hard to meet computational accuracy and reliability requirements of engineering projects,a four-order nonlinear equilibrium differential equation of drill strings expressed by cylindrical coordinates could be numerically solved directly by the differential quadrature element method,and an incremental iteration method was constituted using the arc-length method with DQ elements.Two engineering examples were given to validate the efficiency of this method.The numerical results indicated that the DQ element method could overcome difficulties encountered in dealing with the drill-string weight by the finite element method,and the solution accuracy was significantly improved.Numerical examples revealed that the arc-length iteration method based on DQ elements was characterized by being simple,easy to use,good in convergence,and able to accurately capture the critical load of helical buckling.Therefore,this method can be used readily for the nonlinear buckling analysis of drill strings in slant wells.
出处
《石油学报》
EI
CAS
CSCD
北大核心
2010年第6期1027-1030,共4页
Acta Petrolei Sinica
基金
国家自然科学基金项目(No.10972105)资助
关键词
非线性屈曲
弧长法
DQ单元法
斜直井
非线性微分方程
nonlinear buckling
arc-length method
DQ element method
slant well
nonlinear differential equation
