力学与实践 ›› 2022, Vol. 44 ›› Issue (4): 955-959.DOI: 10.6052/1000-0879-22-013

• 教育研究 • 上一篇    下一篇

塑性力学教学中Mises屈服准则几何轨迹证明

梅瑞斌*(), 包立, 刘相华*   

  1. *. 东北大学材料与科学工程学院,沈阳 110819
    †. 东北大学秦皇岛分校,河北秦皇岛 066004
  • 收稿日期:2022-01-07 出版日期:2022-08-08 发布日期:2022-08-17
  • 作者简介:梅瑞斌,副教授,研究方向为塑性加工工艺与组织性能预测。E-mail: meiruibin@neuq.edu.cn
  • 基金资助:
    河北省教育厅精品课程建设项目(2020JPKC061),东北大学课程思政示范课程(2021KCSZ018)和东北大学秦皇岛分校教改重点项目(2021JG-A03)资助。

PROVING OF YIELD CRITERION OF MISES GEOMETRIC SHAPE IN PLASTIC MECHANICS TEACHING

MEI Ruibin*(), BAO Li, LIU Xianghua*   

  1. *. School of Materials and Engineering, Northeastern University, Shenyang 110819, China
    †. Northeastern University at Qinhuangdao, Qinhuangdao 066004, Hebei, China
  • Received:2022-01-07 Online:2022-08-08 Published:2022-08-17

摘要:

本文针对塑性力学教学中学生难以理解的屈服准则几何轨迹,从教学角度出发,利用坐标变换和空间几何投影关系分析证明了Mises屈服准则的平面椭圆和空间圆柱面轨迹。基于Tresca和Mises屈服准则简化形式,分析了两个准则几何轨迹的内接和外接关系,当用拉伸屈服应力 ${\sigma _{\rm{s}}}$ 表示时,Mises椭圆外接于Tresca六边形,当用剪切屈服强度k表示时,正好相反。

关键词: 屈服准则, 塑性力学, 坐标变换, 几何轨迹

Abstract:

It is difficult for students to understand the yield criterion in the plastic mechanics. The plane ellipse and spatial cylindrical trajectory of Mises yield criterion was proved based on the method of coordinate transformation and geometric projection. Furthermore, from the similarities and differences of mathematical expressions, the internal and external relations and geometric shape of Tresca and Mises yield criterions were investigated in the paper. The research is helpful for students to understand the yield criterion.

Key words: yield criterion, plastic mechanics, coordinate transformation, geometric shape

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