扭矩对三维空间圆截面曲杆弹性屈曲的影响

采用自然坐标系,由Green应变张量的定义,给出了自然坐标形式的三维细长空间曲杆的Green应变计算公式,建立了同时考虑轴向压力和扭矩影响的能量变分方程.采用2节点12个自由度的自然坐标形式的三维空间曲梁单元,采用线性特征值分析方法,研究分析了同时受轴向压力和扭矩作用的具有初始曲率和挠率的三维空间杆柱的屈曲问题.数值结果与存在的理论解极为吻合,验证了公式的正确性.更为引人注意的是:不论直杆还是曲杆,扭矩对它们的弹性屈曲影响不可不计.

Effect of Torque on the Elastic Buckling of 3D Spatial Thin Rods with Circular Cross-sections

The effect of torque on the elastic flexural buckling of 3D spatial thin rods is discussed.The nonlinear terms of the change of tortuosity is usually ignored in geometric nonlinear analysis for thin rods.In other words,it is neglected that the effect of torques on analysis of both the large deflection and the elastic buckling.But in the most extreme cases,the torque may lead to elastic flexural buckling.The effect of torque on geometric nonlinear analysis is not considered in existing commercial FE software.Herein the formulae determining the classical Green strains on the centerline of an initially curved and twisted rod with circular cross-section are given using the natural(curvilinear) coordinate system.It is discussed that finite element analysis of elastic flexural buckling loads from an eigenvalue analysis for initially curved and twisted thin rods under the simultaneous action of axial force and torque.Using the natural coordinate system there will be no necessary to distinguish and transform from local to global coordinate system while the curvature of curved rods is continuous.The formulation is clearly demonstrated by several examples.Some numerical results are well compared with existing theoretical solutions.It is shown that the effect of torques on elastic flexural buckling of 3D both straight and spatial thin rods may be very large and its effect cannot be neglected.