比塑性功求解线性载荷下简支圆板极限载荷  

Analysis of plastic limit load for simply supported circular plate under linear distributed load by specific plastic work

作　　者：章顺虎[1] 赵德文[1] 高彩茹[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,沈阳100819

出　　处：《材料科学与工艺》2012年第5期81-84,89,共5页Materials Science and Technology

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

摘　　要：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a、材料屈服极限σs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之间的变化关系.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.

关 键 词：GM屈服准则 比塑性功 简支圆板 极限载荷 解析解 

分 类 号：TG335.5[金属学及工艺—金属压力加工]