用GM屈服准则解析薄壁筒和球壳的极限载荷

首次将GM(几何中线)屈服准则应用于内压薄壁圆筒和球壳的塑性极限分析,获得了解析解.薄壁筒和球壳极限载荷均为壁厚、内径及材料屈服极限的函数.屈服极限越高、壁厚越大,内径越小,极限载荷越大.与Mises准则、双剪应力准则(TSS)和Tresca准则相比,GM准则解居于TSS和Tresca解之间且靠近Mises解,恰好对应误差三角形中线.按GM准则计算的极限载荷随厚径比的增加而线性增加.

Limit Load of Thin-Walled Cylinder and Spherical Shell with GM Yield Criterion

The GM yield criterion was first applied to analyzing the limit loads of thin-walled cylinder and spherical shell subjected to internal pressure,and the analytical solutions were obtained.The limit loads for both cylinder and spherical shell are the functions of the thickness,diameter as well as the yield strength of the material.The limit loads increase with the increasing of the yield strength and the thickness,and the decreasing of the diameter.Compared with Mises,Tresca and TSS criteria,the solution of GM criterion lies just between the TSS and Tresca solutions,and it is close to Mises solution and just corresponds to the midline of the error triangle.The limit load based on GM criterion increases linearly with the ratio of thinness to diameter.