考虑大位移影响的解析型压扭杆单元  

ANALYTICAL ELEMENT FOR BAR SUBJECTED TO COMPRESSION AND TORSION CONSIDERING THE LARGE DISPLACEMENT

作　　者：许晶[1] 夏文忠 王宏志[1] 蒋秀根[1] XU Jing;XIA Wen-zhong;WANG Hong-zhi;JIANG Xiu-gen(College of Water Resources & Civil Engineering,China Agricultural University,Beijing 100083,China;Power China,Huadong Engineering Corporation Limited,Hangzhou 311122,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]中国电建集团华东勘测设计研究院有限公司,杭州311122

出　　处：《工程力学》2019年第4期44-51,共8页Engineering Mechanics

基　　金：国家自然科学基金项目(51279206);农业部农业设施结构工程重点实验室开放课题(201502);中央高校基本科研业务费专项资金项目(2015SY004)

摘　　要：为提高压扭杆件内力和变形分析的精度和效率,以Vlasov扭转理论为基础,根据压扭杆件位移控制方程,考虑大位移和截面翘曲影响,构建了压扭杆的单元位移形函数,采用势能原理建立了压扭杆势能泛函。利用势能驻值变分原理得出了解析型压扭杆单元列式,并推导了用于杆件内力分析的单元刚度矩阵。将其与理论解、插值多项式单元进行对比,结果表明:该文构造的单元计算压扭杆转角及翘曲率和临界荷载的精度高于插值多项式单元,且不需划分单元,即可保证计算结果与理论解一致,满足了高精度、高效率的要求,可应用于解决实际工程问题。To improve the accuracy and efficiency in calculating the inter force and deformation of bar under compression and torsion, the shape function was determined by considering the section warping and the effect of large displacement, based on Vlasov restrained torsion theory and according to the displacement controlling equation for bar. Potential energy functional of bar subjected to compression and torsion was established by applying potential energy principle. Analytical element formulations for bar were received and element stiffness matrix was obtained via variational principle of potential energy stationary value. Comparisons among the calculation results of proposed element, theoretical solution, and interpolation polynomial element are conducted, and the results show that the solution of analytical element by one element number is in accordance with the theoretical solution. The analytical element can satisfy the high accuracy and efficiency requirement and can be applied in practice.

关 键 词：压扭 解析形函数 变分原理 有限元 单元刚度矩阵 

分 类 号：TB125[理学—工程力学]