MY准则解线性和均布载荷下简支圆板的极限载荷

Limit Load Analysis of Simply Supported Circular Plate Under Linearly and Uniformly Distributed Load with MY Criterion

用平均屈服(MY)准则,对受线性和均布载荷共同作用下的简支圆板进行塑性极限分析,求得了2种载荷形式下极限载荷的解析解.两解析解均为圆板半径a,切向应力最大点半径r0以及极限弯矩的函数.第一种形式的计算结果与Tresca,Mises和TSS屈服准则预测的极限载荷比较表明,Tresca屈服准则预测极限载荷的下限,TSS屈服准则预测极限载荷的上限,MY准则预测的极限载荷居二者中间,并靠近Mises解.另外还讨论了圆板半径对切向应力最大点半径的影响规律.

With MY（mean yield） criterion, the limit loads of simply supported circular plate under linearly and uniformly distributed load were analyzed, and two analytical solutions to two forms of loads were obtained. The solutions showed that both the limit loads are the function of circular plate radius a, radius of the maximum tangential stress location r0 and ultimate bending moment. The limit load of the first form calculated by the solution is compared with those based on Tresca, Mises, as well as TSS yield criteria. It is shown that Tresca criterion predicts a lower bound to the collapse load, while TSS criterion predicts an upper bound one. The limit load based on the MY criterion lies between the TSS and Tresca solutions, and the MY solution is closed to Mises solution. Besides, the effect of circular plate radius a on r0 is also discussed.