水平圆管中受压扭作用管桩屈曲后的解析解

AN ANALYTIC SOLUTION FOR POST-BUCKLING OF TUBULARS SUBJECTED TO AXIAL AND TORSIONAL LOADING IN HORIZONTAL CIRCULAR CYLINDERS

首先建立了考虑自重、受水平圆管约束的管柱在压担组合作用下的屈曲方程：此方程为四阶强非线性常微分方程，难以直接精确求解；通过管柱的正弦屈由分析，找到了方程中的小参数；利用小参数摄动法求解了强非线性屈曲方程，得到了管柱螺旋屈曲后的实际屈曲构形解析解，由此可进一步得到管柱发生螺旋屈曲的临界载荷；所得解析结果与数值计算结果及本文结果退化后与文献中的相关结果比较都有良好的一致性．

Buckling of radially confined oil tubulars is of significant importance to the oil industry.It will affect the life of the tubulars and cause difficulties in drilling and in oil production. Anumber of theoretical models have been developed to study the buckling load and the post-bucklingconfiguration of the tubular, but the most of the past studies have not considered the torsionalloads. Only recently, some investigators based on energy principle have derived some results forbelieal buckling of tubulars subjected to axial and torsional loading. The underlying assumptionfor current energy method is that the helix pitch of the belieal buckling shape is constant. However,it is difficult to obtain real post-buckling configuration by the energy methods.In this paper, the buckling equation for a buckled tubing subjected to axial and torsionalloading in horizontal circular cylinder is derived. The equation is a fourth-order strongly nonlinearordinary differential equation, and it is too difficult to solve it exactly. So a small parameter in theequation is determined by discussing the initiate sinusoidal buckling of the tubular. If the parameteris set to zero, the equation that describe the belieal buckling for the case of weightless tubulars is stillnonlinear but the exact solution have been derived. Using perturbation method 3 an approximateanalytical solution for the equation that describe the real belieal buckling configuration of tubularwith weight have been derived. Based on the solution, the critical belieal buckling load can bedetermined. The analytical results obtained by this paper well coincide with the results obtained bynumerical method. The degenerative results of the analytical results obtained are also coincidentwith those given by others using energy method.