弹性直杆中一类动力屈曲问题的渐近解

The Asymptotic Solution of a Dynamic Buckling Problem in Elastic Columns

对于弹性杆受刚性块轴向撞击的动力屈曲问题而言，由于轴向载荷形式较为复杂，问题将归结为关于非线性偏微分方程组解的讨论，至今仍未能得到一个理论上的解析解，为此，讨论了有限长理想弹性直杆的此类动力屈曲问题，采用小参数的摄动展开和变分法，成功地得到了这一问题的一个理论上的近似解，并给出了相应的算例，从中得到了一些有益的结论·

For the dynamic buckling of an elastic column, which is subjected to a longitudinal impact by a rigid body, the form of the axial load is very complicated. The problem may be reduced to discuss the solution of nonlinear partial differential equations. So far, a theoretical solution may not be obtained. In this paper, this dynamic buckling problem of an ideal elastic column with finite length is discussed. By the perturbation method with a small parameter and the variational method, a solution of this problem is given. Finally, numerical computation is carried out, from this, some beneficial conclusions are obtained.