A numerical study of necking in circular cylindrical bar
A numerical study of necking in circular cylindrical bar
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DOI：
10.1016/0022-5096(72)90035-x
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发表时间：
1972-05
影响因子：
5.3
通讯作者：
A. Needleman
中科院分区：
文献类型：
--
作者：
A. Needleman
用两种方法给出了圆柱杆在单轴拉伸作用下的边值问题。在其中一处，假定试样的两端被粘接到刚性握把上；而在另一种情况下，它们保持剪切自由。在后一种结束条件下，颈缩是由均匀拉应力状态的分叉引起的。利用有限元方法求解了控制分岔的特征值问题，并将所得结果与传统的最大荷载准则进行了比较。然后确定分叉后的行为。计算了粘接杆的整个变形过程，并评估了端部条件对后弯杆变形的影响。
Theboundary-value problem for a circular cylindrical bar in uniaxial tension is posed in two ways. In one the ends of the specimen are assumed to be cemented to rigid grips; while in the other they remain shear free. With the latter end-condition, necking initiates by a bifurcation from a state of uniform tensile stress. The eigenvalue problem governing bifurcation is solved by means of the finite element method, and a comparison is made between the results obtained here and the conventional maximum load criterion. The post-bifurcation behavior is then determined. The entire deformation history of the bar cemented to rigid grips is also calculated and the effect of end conditions on the deformations in the necked-down bar is assessed.