空间薄壁梁完全拉格朗日格式几何刚度矩阵

根据Timoshenko梁理论和Vlasov薄壁杆件理论,通过设置单元内部节点,对弯曲转角和翘曲角采取独立插值的方法,建立了可以考虑剪切变形、弯扭耦合和二次剪应力影响的空间薄壁截面梁几何非线性有限元模型。以拉格朗日格式描述几何非线性应变推得几何刚度矩阵.算例表明所建立模型具有良好的精度,适用于空间薄壁结构的几何非线性有限元分析.

Geometrical Stiffness Matrix of Spatial Thin walled Beams in Total Lagrangian Formulation

Based on the theories of Timoshenko’s beams and Vlasov’s thin-walled members,a new geometrically nonlinear beam element model is developed by placing an interior node in the element and applying independent interpolation to bending angles and warp,in which factors such as shear deformation,coupling of flexure and torsion,and second shear stress are all considered.Thereafter,geometrical nonlinear strain in Total-Lagrangian is formulated and geometrical stiffness matrix is deduced.Examples manifest that the developed model is accurate and feasible in analyzing thin-walled structures.