新型空间薄壁梁单元  

New Finite Element of Spatial Thin-Walled Beams

作　　者：王晓峰[1] 张其林[1] 杨庆山[2] 

机构地区：[1]同济大学土木学院,上海200092 [2]北京交通大学土建学院,北京100044

出　　处：《应用数学和力学》2010年第9期1089-1100,共12页Applied Mathematics and Mechanics

基　　金：国家科技支撑计划资助项目(住宅结构与构造选型设计技术与软件开发;2008BAJ08B06);国家高技术研究(863计划)发展计划资助项目(2009AA04Z420);国家自然科学基金杰出青年基金资助项目(50725826);上海市博士后科研基金资助项目(10R21416200)

摘　　要：基于Timoshenko梁理论和Vlasov薄壁杆件约束扭转理论,建立了具有内部结点的新型空间薄壁截面梁单元.通过对弯曲转角和翘曲角采取独立插值的方法,考虑了横向剪切变形,扭转剪切变形及其耦合作用,弯曲变形和扭转变形的耦合以及二次剪应力等因素影响,由Hellinger-Reiss-ner广义变分原理,推得单元刚度矩阵.算例表明所建模型具有良好的精度,可用于空间薄壁杆系结构的有限元分析.Based on the theories of Timoshenko＇s beams and Vlasov＇s thin-walled members,a new spatial thin-walled beam element with an interior node was developed.By independently interpolating bending angles and warp,factors such as transverse shear deformation,torsional shear deformation and their coupling,coupling of flexure and torsion,and second shear stress were all considered.According to the generalized variational theory of Hellinger-Reissner,the element stiffness matrix was deduced.Examples manifest that the developed model is accurate and can be applied in the finite element analysis of thin-walled structures.

关 键 词：空间梁 薄壁截面 刚度矩阵 剪切变形 弯扭耦合 二次剪应力 

分 类 号：TU323.3[建筑科学—结构工程]