矩形厚板弹塑性屈曲的微分求积法分析  

Elastoplastic Buckling Analysis of Thick Rectangular Plates by Using the Differential Quadrature Method

作　　者：张伟[1] 王鑫伟[1] 

机构地区：[1]南京航空航天大学结构与强度研究所飞行器结构力学与控制教育部重点实验室,南京210016

出　　处：《机械科学与技术》2011年第4期538-542,共5页Mechanical Science and Technology for Aerospace Engineering

基　　金：国家自然科学基金(50675100)资助

摘　　要：笔者首次采用微分求积法分析了矩形厚板的弹塑性屈曲问题。为了考虑横向剪切变形的影响,采用了Mindlin板理论和全量理论和增量理论,推导了相应的控制微分方程与内力的表达式。为了验证所推导的公式和求解算法,将本文结果与现有文献中的结果(包括精确解)进行了对比,然后给出了一些新的结果,并指出了两种理论结果之间差异大的原因是由于增量理论产生了大的等效应变从而违反了建立方程时的小变形假设,因此增量理论得到的结果是不可信的结果。We investigate the elastoplastic buckling behavior of thick rectangular plates by using the differential quadrature（DQ） method for the first time.Mindlin plate theory is adopted to take the transverse shear effect into consideration.Both incremental theory（IT） and deformation theory（DT） are adopted.The derivations of the governing differential equations and the expressions of the internal forces are described in detail.To verify the derived equations and solution procedures,the DQ results are first compared with the existing results including the exact solutions.Then,some new results are provided.The effective strains obtained by IT are too large to happen in practice and the small deformation assumption is violated;it is the possible reason to cause the large discrepancy between the data obtained by the two theories.The present research extends the application range of the differential quadrature method.

关 键 词：弹塑性 矩形厚板 MINDLIN板理论 微分求积法 屈曲 

分 类 号：O344.7[理学—固体力学]