复合受载下简支矩形板屈曲分析的微分求积法  

Buckling Analysis of Simply Supported Rectangular Plates Under Compound Load by Differential Quadrature Method

作　　者：付为刚[1] 程文明[1] 濮德璋[1] 任扬志[1] 

机构地区：[1]西南交通大学机械工程研究所,成都610031

出　　处：《机械设计与研究》2012年第5期103-106,共4页Machine Design And Research

基　　金：国家自然科学基金资助项目(51175442;51205328);中央高校基本科研业务费专项资金资助项目(2010ZT03)

摘　　要：为了精确求解复合受载下简支矩形板屈曲失稳的问题。推导简支矩形板无量纲屈曲微分方程,给出简支矩形板屈曲分析的微分求积计算格式。以单(双)向轴压作用下的简支矩形板为例,通过与解析解、有限元解对比验证微分求积法求解简支矩形板屈曲失稳问题的精确性。以轴压和剪应力作用下的简支矩形板为例,通过同解析解对比分析表明,当边长比r=1～5时,解析解与数值解间的差别较小;当边长比r=1/5～1时,解析解随方程数N的增大而逐步逼近数值解。To solve accurately the buckling of simply supported rectangular plates,the dimensionless derivations of bucking balance differential equations for such rectangular plates is also given when it is affected by the longitudinal load.Besides,the calculation procedures are described in detail when the differential quadrature methods（DQM） are used to solve the critical buckling load of such plates.Then,the elastic rectangular plate subjected to uniaxial or biaxial loading condition is considered to verify the accuracy of DQM solution procedures.Finally,the elastic rectangular plate subjected to shear force and uniaxial load is taken as the case study.Via the comparison between the analytic solution and the DQM solution,when the aspect ratio is from 1 to 5,there is little difference between the above two solutions,and when the aspect ratio is from 1/5 to 1,the difference between them decreases with increasing the number of equation for the analytic solution.

关 键 词：起重机 简支板 屈曲 微分求积法 

分 类 号：TH213.5[机械工程—机械制造及自动化]