MY准则解析受均布载荷简支斜板极限载荷

摘要

为了得到斜板极限载荷的解析解,用平均屈服（MY）准则,对受均布载荷的简支金属斜板进行了塑性极限分析.首次获得MY准则下斜板极限载荷的解析解,该解是斜板几何参数长l1,宽l2以及长宽夹角θ的函数.研究表明：随着θ的增大,极限载荷先增大而后减小;斜板面积增加,极限载荷减小.得到了菱形、矩形和方形板的解析解,并将方形板的解析解与Tresca、Mises以及TSS提供的极限载荷进行比较,对比表明：方板的极限载荷与边长成反比关系,Tresca屈服准则提供极限载荷的下限,TSS屈服准则提供上限,MY准则预测结果恰居二者中间,且最靠近Mises解.%To obtain an analytical solution of the problem of plastic limit load of simply supported skew plate,the simply supported skew plate under uniformed loading is analyzed with MY（mean yield） criterion.The solution shows that the limit load is a function of skew plate length l1,width l2 and intersection θ,which increases first and then decreases as the intersection θ increases,and decreases with the increasing of the skew plate area.What＇s more,the solutions of diamond,rectangular and square plates are also deduced.The limit load of square plate calculated by MY solution is compared with those based on Tresca,Mises,as well as TSS yield criteria.The relationship between the limit load of the square plate and the side length of the plate is inverse,and the Tresca criterion predicts a lower bound of the limit load,while the TSS criterion predicts an upper bound.However,the limit load by the MY criterion lies just between the TSS and Tresca solutions,and the MY criterion is most close to Mises solution.