Geometrically Nonlinear Analysis of 2-D Corotaional Timoshenko Beam Element
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摘要: 改进了独立于单元的共旋(EICR)二维梁列式,使得不必再重新推导局部共旋标架下的单元材料刚阵,该列式可直接将现有性能良好的线性梁单元扩展用于二维梁结构任意大转动的几何非线性分析,同时推导了随动压强载荷作用引起的载荷刚度项,确保了高效的收敛速率。基于二维EICR梁列式将一种工程中实用的铁摩辛柯梁单元扩展用于几何非线性分析,数值算例表明文中所提共旋列式的铁摩辛柯梁单元计算精度高、计算效率高,可用于二维梁结构的几何非线性优化。Abstract: This paper improves the element independent corotaional (EICR) formula, with which it is not necessary to derive the stillness of materials in the local corotational coordinate system. The formula can extend the existingrobust linear beam element to deal with the arbitrarily large rotation in the geometrical nonlinear analysis of 2-D corotational Timoshenko beam element. Meanwhile the load stiffness that results from follower load was deduced, andthe high convergence speed was retained. The geometrical nonlinear analysis of one of the Timoshenko beam elements was carried out, using the EICR formula. The numerical example shows that the corotaional Timoshenkobeam element analysis method is accurate, efficient and applicable to the geometrically nonlinear optimization of a2-D beam structure.
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