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基于共旋列式的空间梁的稳定性分析
引用本文:王振,孙秦.基于共旋列式的空间梁的稳定性分析[J].固体力学学报,2014,35(1):49-56.
作者姓名:王振  孙秦
作者单位:西北工业大学
摘    要:基于独立于单元的共旋列式(EICR),将一种几何线性的无剪切锁死的Timoshenko梁单元扩展用于空间梁结构的几何非线性分析。考虑到三维分析中发生大转动时转动顺序的不可交换性,也即转动自由度不能作为向量采用加法规则更新,采用了四元变量来存储和更新转动自由度,使得共旋列式适用于位移任意大和转动任意大但应变很小的几何非线性分析。同时改进了Riks弧长法使之适用于带有大转动的三维几何非线性分析。给出了几个数值算例,结果表明本文方法具有较高的计算精度和效率。

关 键 词:几何非线性  共旋列式  大转动  Riks弧长法  Timoshenko梁单元  geometrical  nonlinear    EICR    large  rotation    Riks  arc-length  method    Timoshenko  beam  element  
收稿时间:2013-01-07

Stability analysis of spatial beam based on corotational formulation
Abstract:Based on the element independent corotational formulation (EICR), a geometrically linear shear locking free Timoshenko beam element was extended to the geometrically nonlinear analysis of spatial beams with arbitrarily large displacements and rotations but small strain. On considering the non-communitativity of finite rotations in three-dimensional analysis, which means that rotational degrees of freedom can't be updated by addition rule as vector quantities, therefore, the quaternion was used to store and update the rotational degrees of freedom. And a modified Riks arc-length method suitable for three-dimensional geometrically nonlinear analysis with large rotations was also presented. Several numerical examples for geometrical nonlinear analysis of spatial beams using the present beam element were also presented and the results demonstrate that the proposed element and methods are efficient and accurate.
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