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本文对截面具有两个不相等主惯性矩的海洋石油立管的三向大位移分析作了理论推导。在推导中,全面考虑了立管弯曲、扭转和拉伸变形。通过综合立管轴向的平衡条件和能量泛函的驻值条件,得出了独特的混合方法。平衡状态时立管中心线的孤长s取为自变量,而立管中心线的坐标X、Y和截面扭转角F以及管内拉力T则为孤长s的函数。在上述理论推导的基础上,形成了求解具有二相等主惯性矩的立管三向六位移分析的有限元方法。根据此方法编写了计算机程序,并给出了算例。
This paper makes a theoretical derivation of the three-dimensional large displacement analysis of offshore petroleum risers with two unequal principal moments of inertia in the section. In the derivation, the bending, torsion, and tensile deformations of the riser were fully considered. By integrating the axial equilibrium conditions of the riser and the resident conditions of the energy functional, a unique hybrid method was obtained. In the equilibrium state, the lone length of the centerline of the riser is taken as the independent variable, and the coordinates X, Y of the centerline of the riser, the cross-sectional angle of twist F, and the tension T in the tube are the functions of the lenght s. Based on the above theoretical derivation, a finite element method is developed to solve the three-way six-displacement analysis of risers with two equal principal moments of inertia. A computer program was written according to this method and an example was given.