直杆中应力波传播引起的分叉问题

AbstractBIFURCATION CAUSED BY THE STRESS WAVE IN COLUMNS 1)

讨论轴向矩形脉冲载荷作用下有限长理想弹性直杆中应力波的传播及其反射引起的分叉问题，讨论此类动力屈曲问题中横向惯性效应的影响；理论分析始终遵循着这样的思路：在分叉的那一瞬间，杆并没有横向惯性效应，目的是给出此类问题的一个合理提法，从理论分析和数值计算中得到了许多重要的结论，理论分析所遵循的思路和所采用的方法对各类结构由于应力波的传播及反射引起的分叉问题具有一定的意义．

The elastic or plastic dynamic buckling of columns under different kinds of axial impact loading has been studied for a long time. When studying this problem, most researchers usually assume that the column has some imperfections and analyze the developing course of this imperfection under impact load by the amplification function method. Although the method is very practical in engineering, it has some defects. On the one hand, the bifurcation problem is analyzed like a strength or stiffness one, so its essential pecularity is covered up, on the other hand, the amplification is given as one pleases, when the plastic buckling is concerned, and if the amplification is larger, we should pay attention to the fact whether Shanley's hypothesis is true or not. A few reports on the dynamic buckling considering the effect of stress wave have been found, but the reflection of stress wave are not taken into consideration up to now. In this paper, the bifurcation problem of an elastic coumn with finite length is studied. It’s dynamic buckling under the rectangular load is reduced to a bifurcation problem caused by the propagation of axial stress wave. The critical buckling condition is given with reflection of the elastic stress wave being taken into account. The lateral inertia effect is discussed. The theoretical analysis shows that at the instant when the bifurcation occurs there is not any lateral inertia effect. Numerical computation and conclusions are presented.