Plastic analysis of torsion of a prismatic beam
Plastic analysis of torsion of a prismatic beam
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棱柱梁扭转的塑性分析
DOI：
10.1002/nme.1620180609
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发表时间：
1982
影响因子：
2.9
通讯作者：
T. Kajita
中科院分区：
文献类型：
--
作者：
S. Baba;T. Kajita
建立了扭梁应力分析的有限元公式。该公式对实截面棱柱梁和薄壁梁均有效，可用于纯扭转问题和翘曲扭转问题。该公式对弹塑性扭转问题有很大的帮助。该公式没有建立在薄壁结构的假设上，因此可以在不使用所谓的圣维南扭转常数的情况下准确地评估截面的扭转刚度。在本文中，扭转刚度是由截面的翘曲函数直接评估的。由于截面的形状、塑性区域的进展以及有限位移（有限旋转、小应变）的影响，对翘曲函数进行了数值计算。分析了具有弹塑性材料特性的矩形梁和h型梁的纯扭转和翘曲扭转问题，并讨论了其对有限位移问题的推广。为了验证该公式的准确性，给出了许多数值算例。
Finite element formulation for stress analysis of a twisting beam is developed. The formulation is effective for a prismatic beam with solid section as well as a thin-walled beam, and can be applied both to a pure-torsion problem and a warping-torsion problem. The formulation is of a great advantage to an elastic-plastic torsion problem. The formulation does not stand on the assumption of a thin-walled structure, and therefore torsional rigidity of the section can be evaluated exactly without using the so-called Saint-Venant's torsional constant. Torsional rigidity is, in this paper, evaluated directly by a warping function of the section. Warping function is evaluated numerically due to shape of the section, due to progress of plastic region and due to effect of finite displacement (finite rotation, small strain). Pure-torsion and warping-torsion of a rectangular beam and an H-beam, which have an elastic-plastic material property, are analysed, and the extension to the finite displacement problem is discussed. Many numerical examples are provided in order to check the accuracy of the formulation.