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为了保证能量泛函驻立值与平衡微分方程本征值间的一致性,基于平衡微分方程及自然边界条件,构建了受径向约束杆柱的DQ(Differential Quadrature)单元。对于受圆形管柱约束的一段杆柱,分析了九种不同端部约束条件下的正弦屈曲载荷,与现有文献中的解析解和实验结果比较表明,该文的模型及分析方法是合理的。对斜直井内的一段钻柱,通过数值分析,考察了井斜角和端部约束等因素对钻柱正弦屈曲的影响。同时,与有限元结果比较证实,分析斜直井内钻柱屈曲的DQ单元精度高,可靠性强。给出了一些有工程参考意义的结论。
In order to ensure the consistency between the eigenvalues of energy functional stationary and equilibrium differential equations, a DQ (Differential Quadrature) element constrained with radially constrained rods is constructed based on equilibrium differential equations and natural boundary conditions. For a section of column constrained by a circular column, the sinusoidal buckling loads under nine different kinds of end constraints are analyzed. Compared with the analytical solutions and experimental results in the existing literature, the model and analytical method of the paper are reasonable of. For a section of drill string in a vertical well, the influence of well inclination and end constraint on the sinusoidal buckling of the drill string was investigated by numerical analysis. At the same time, compared with the finite element results, it is proved that the analysis of the buckling of the drill string in the inclined well has high accuracy and reliability. Some conclusions about the significance of engineering reference are given.