比塑性功求解线性载荷下简支圆板极限载荷-哈尔滨工业大学学报.PDF

第20卷摇 第5期 材摇 料摇 科摇 学摇 与摇 工摇 艺 Vol.20 No.5 摇 摇 20 12年10月 MATERIALS SCIENCE TECHNOLOGY Oct. ,2012 摇 摇 摇 摇 摇 摇 比塑性功求解线性载荷下简支圆板极限载荷 章顺虎,赵德文,高彩茹,王国栋 (东北大学 轧制技术及连轧自动化国家重点实验室,沈阳100819) 摘摇 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 及板厚h 的函数.与Tresca、TSS及Mises预测的极限 滓 s 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. 关键词:GM屈服准则;比塑性功;简支圆板;极限载荷;解析解 中图分类号:TG335.5 文献标志码:A 文章编号:1005-0299(2012)05-0081-04 Analysis of plastic limit load for simply supported circular plate under linear distributed load by specific plastic work ZHANG Shun鄄hu,ZHAO De鄄wen,GAO Cai鄄ru,WANG Guo鄄dong (State Key Laboratory of Rolling and Automation,Northeastern University,Shenyang 100819,China) Abstract:To obtain an analytical solution of plastic limit load of simply supported skew plate,the plastic limit load of simply supportedskew plateunderlinearly distributedloadingisanalyzedwiththespecificplasticwork rate of GM (geometrical mid鄄line) criterion.The analytical solution based on the GM criterion is first ob鄄 tained.The solution shows that the limit load is afunction of the radiusa,the thicknessh and the yield stress 滓 of the plate.The limit loads calculated by the solutions are compared with those based on Tresca,TSS ands Misesyield criteria,and the result shows that Tresca criterion predicts a lower bound to the limit load,while TSS crit