均布载荷作用下简支圆板塑性极限载荷的解析解  

ANALYTICAL SOLUTION OF PLASTIC LIMIT LOAD FOR SIMPLY SUPPORTED CIRCULAR PLATE UNDER UNIFORMLY DISTRIBUTED LOAD

作　　者：章顺虎[1] 高彩茹[1] 李秀玲[1] 赵德文[1] 王国栋[1] 

机构地区：[1]东北大学轧制技术及连轧自动化国家重点实验室,辽宁沈阳110819

出　　处：《工程力学》2013年第3期53-57,共5页Engineering Mechanics

基　　金：国家自然科学基金项目(51074052);中央高校基本科研业务费项目(N110607002)

摘　　要：该文建立了受均布载荷作用简支圆板运动许可应变场,并首次以EA(等面积)屈服准则进行了塑性极限分析,获得了极限载荷的解析解。该解为圆板半径a、圆板厚度h以及屈服强度的函数。与Tresca、TSS以及Mises解比较表明,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,EA和Mises屈服准则预测的极限载荷恰居二者中间,且EA解几乎与Mises解重合。此外,该文还讨论了挠度与相对位置r/a之间的变化关系。A kinematic admissible strain field for a simply supported circular plate under a uniformly distributed load is proposed, the plastic limit analysis is first carried out with an EA （equal area） yield criterion and an analytical solution is first obtained. The solution shows that the limit load is a function of a circular plate with radius of a, the circular plate thickness of h and yield stress. The limit load calculated by the solution is compared with those based on Tresca, TSS and Mises yield criteria. 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 EA and Mises criteria lies just between the TSS and Tresca solutions; most notably, the EA solution almost has the same calculating precision with Mises solution. Besides, the relationship between deflection and relative position is also discussed.

关 键 词：极限载荷 均布荷载 EA屈服准则 解析解 简支圆板 

分 类 号：TG301[金属学及工艺—金属压力加工]