为了获得线性载荷作用下的简支圆板极限载荷的解析解，本文提出了刚塑性第一变分原理的运动许可应变场，并首次以GM（几何中线）屈服准则塑性比功进行了塑性极限分析，首次获得了GM准则下圆板极限载荷的解析解，该解为圆板半径n、材料屈服极限σ，及板厚h的函数，与Tresca、TSS及Mises预测的极限载荷比较表明：Tresca准则预测极限荷载下限，TSS屈服准则预测极限载荷的上限，GM屈服准则比塑性功解析结果恰居于两者之间；GM解略低于Mises解，两者相对误差为3．38％．此外，文中还讨论了挠度与相对位置r／a之间的交化关系。
To obtain an analytical solution of plastic limit load of simply supported skew plate, the plastic limit load of simply supported skew plate under linearly distributed loading is analyzed with the specific plastic work rate of GM ( geometrical mid-line ) criterion. The analytical solution based on the GM criterion is first obtained. The solution shows that the limit load is a function of the radius a, the thickness h and the yield stress σ, of the plate. The limit loads calculated by the solutions are compared with those based on Tresca, TSS and Mises yield criteria, and the result shows that Tresca criterion predicts a lower bound to the limit load, while TSS criterion predicts an upper bound one. The limit load based on the GM criterion lies just between the TSS and Tresca solutionsmost notably, the GM solution is a little lower than that based on Mises yield criterion and the relative error between them is about 3.38%. Besides, the relationship between deflection and relative position is also discussed.
参考文献
| [1] | G. Ma;H. Hao;S. Iwasaki .Unified plastic limit analyses of circular plates under arbitrary load[J].Journal of Applied Mechanics,1999(2):568-570. |
| [2] | 赵德文,谢英杰,刘相华,王国栋.由Tresca和双剪应力两轨迹间误差三角形中线确定的屈服方程[J].东北大学学报(自然科学版),2004(02):121-124. |
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