空间薄壁截面梁非线性有限单元模型

A NEW NONLINEAR FINITE ELEMENT MODEL FOR SPATIAL THIN-WALLED BEAMS

基于Timoshenko梁理论和Vlasov薄壁杆件理论,通过设置单元内部节点并对弯曲转角和翘曲角采取独立插值的方法,建立了可考虑横向剪切变形和扭转剪切变形及其耦合作用、弯扭耦合、以及二次剪应力影响的空间薄壁梁非线性有限元模型。以更新的拉格朗日格式描述的几何非线性应变推得几何刚度矩阵。同时考虑了材料非线性,假定材料为理想塑性体,服从Von Mises屈服准则和Prandtle-Reuss增量关系,采用有限分割法,由数值积分得到空间薄壁梁的弹塑性刚度矩阵。算例表明该文所建梁单元模型具有良好的精度,适用于空间薄壁结构的有限元分析。

Based on the theories of Timoshenko＇s beams and Vlasov＇s thin-walled members,a new nonlinear beam element model is developed by placing an interior node in the element and applying independent interpolation on bending angles and warping angles,in which factors such as traverse shear deformation,torsional shear deformation and their coupling,coupling of flexure and torsion,and second shear stress are all considered.According to nonlinear strain in Updated Lagrangian formulation,geometrical stiffness matrix is deduced.In the aspect of physical nonlinearity,the perfectly plastic model is applied and the yield rule of Von Mises and incremental relationship of Prandtle-Reuss are adopted.Elastoplastic stiffness matrix is obtained by numerical integration on the basis of the finite segment method.Examples show that the developed model is accurate and can be applied to the analysis of thin-walled structures.