考虑弯扭耦合的解析型薄壁梁单元  

Analytical element for thin-walled beam considering coupling of bending and torsion

作　　者：许晶[1] 夏文忠 王宏志[1] 蒋秀根[1] XU Jing;XIA Wenzhong;WANG Hongzhi;JIANG Xiugen(College of Water Resources & Civil Engineering, China Agricultural University, Beijing 100083 , China;Huadong Engineering Corporation Limited, Power China, 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,浙江杭州311122

出　　处：《建筑结构学报》2019年第6期140-146,共7页Journal of Building Structures

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(2015SY004)

摘　　要：为提高分析薄壁梁杆件弯扭问题的精度和效率,以Vlasov薄壁杆件理论为基础,考虑大位移和截面翘曲的影响,建立弯扭杆件位移控制方程,构造了薄壁梁杆单元的解析位移形函数,采用势能原理建立了薄壁梁杆势能泛函。利用势能驻值变分原理构造了用于内力分析的解析型薄壁梁杆单元列式,给出了解析型单元刚度矩阵,将其与理论解、插值多项式弯扭杆单元进行对比分析。结果表明,采用构造的解析型单元计算的薄壁梁扭转角及翘曲率的精度远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的相对误差在0. 065%之内,可用于开口薄壁杆件结构的弯扭耦合受力分析及稳定计算。To improve the accuracy and efficiency of analysis of thin-walled beams under combined bending and torsion,the displacement controlled equation was established based on the Vlasov’s thin-walled member principle,considering the influence of large deformation and warping. The analytical shape function for thin-walled beams was then determined. The potential energy function of thin-walled beams was established by applying the potential energy principle. Analytical element formulations and the stiffness matrix of analytical element for thin-walled beams were obtained via the variational principle of potential energy stationary value. The calculation results of the proposed element,the theoretical solution,and the interpolation polynomial element were compared and analyzed. The results show that the accuracy of the proposed element on calculating the torsional angle and warp rate is significantly higher than that of the interpolation polynomial method. The relative error between the solution of the analytical element and the theoretical solution is less than 0. 065% when only one single element is used. The analytical element can be applied to solve the problems of force analysis and stable calculation for open thin-walled frame structures considering the coupling of bending and torsion.

关 键 词：薄壁梁 弯扭耦合 解析形函数 变分原理 单元刚度矩阵 

分 类 号：TU323.3[建筑科学—结构工程]