摘要
对稳定材料来说,在应力π平面上,双剪应力屈服准则[1]为所有屈服准则的外包络线,Mohr-Coulomb屈服准则为所有屈服准则的内包络线(当材料的单向拉伸强度与单向压缩强度相等时,Mohr-Coulomb屈服准则退化为广义Tresca屈服准则).但关于此问题的严格数学证明却还是空白.本文作者通过引入凸集概念,对上述问题做出了数学上的严格证明.
Twin shear stress,yield criterion is the exterior envelope and Mohr-Coulomb yield criterion is the interior envelope of all the yield criteria of the stable material on the stress π plane (if the strength of simple extension test equals that of simple compression test,Mohr-Coulomb yield criterion degenerates into extensive Tresca criterion). But there is still a blank in the area of the strict mathematical proof of this problem.In this paper,the authors solve the problem by citing the mathematical concept of convex set.
关键词
稳定材料
π平面
屈服曲线
包络线
应力
stable material
π plane
yield curve
envelope
convex set
supporting hyperplane