考虑弯曲位移影响的解析型压杆单元构造  

Analytical element for compressive bar considering flexural displacement

作　　者：许晶[1] 汤丽锋 王宏志[1] 曹琼琼 蒋秀根[1] XU Jing;TANG Lifeng;WANG Hongzhi;CAO Qiongqiong;JIANG Xiugen(College of Water Resources & Civil Engineering,China Agricultural University,Beijing 100083,China;Shanghai Construction Design & Research Institute Co.,Ltd.,Shanghai 200235,China)

机构地区：[1]中国农业大学水利与土木工程学院,北京100083 [2]上海市建工设计研究总院有限公司,上海200235

出　　处：《江苏大学学报（自然科学版）》2019年第2期167-171,共5页Journal of Jiangsu University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11272340);中央高校基本科研业务费专项(2014XJ037)

摘　　要：利用解析形函数构造了压杆单元,可用于求解压杆稳定问题.基于考虑二阶效应影响的压杆微分平衡方程,得到以节点位移表示的压杆位移形函数,利用能量法和解析形函数得到压杆单元势能泛函表达式.对压杆单元势能泛函变分,确定了考虑弯曲位移影响的压杆单元弹性刚度矩阵和几何刚度矩阵.为检验解析型压杆单元的精度,将提出的方法与插值形函数法和直接刚度法进行对比,结果表明:提出的解析型压杆单元具有较高的计算精度和效率.The element for compressive bar was constructed to deal with the stability problems by analytical shape function. Considering the second order effect,the equilibrium differential governing equation of compressive bar was established,and the corresponding displacement shape functions were derived and expressed by node displacement. The potential energy functional expression for compressive bar element was developed by potential energy principle and analytical shape function. Considering the effect of flexural displacement,the elastic and geometrical stiffness matrices were proposed through the variation of total potential energy. To verify the precision of the proposed element,the numerical comparisons were conducted among the interpolation shape function method,the direct stiffness method and the analytical shape function method. The results show that the proposed element has high calculation precision and efficiency.

关 键 词：压杆 最小势能原理 解析形函数 有限元 位移 

分 类 号：TU311[建筑科学—结构工程]