New Finite Element of Spatial Thin-Walled Beams
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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-Reissner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.Abstract: 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.
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