Updated Lagrangian Co-rotational Formulation for Geometrically Nonlinear FE Analysis of 3-D Beam Element
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摘要: 为了提高大位移、大转动问题的计算效率和精度,提出了基于更新拉格朗日法(UL法)的三维梁单元分析的CR列式算法.这种方法采用更新拉格朗日列式,运用最小势能原理建立结构的平衡方程,并导出梁单元的刚度矩阵.求解过程中,根据CR列式的原理,采用大转动理论计算更新后的单元和节点坐标,通过扣除结构位移中的刚体位移得到结构变形,进而获得单元的准确内力.最后,给出了2个算例,以证明该方法的正确性和精度.Abstract: To improve the precision and efficiency of computations for a structure with a large displacement and rotation,an updated Lagrangian co-rotational formulation for geometrically nonlinear FE(finite element) analysis of 3-D beam elements was proposed.With this method,a standard updated Lagrangian formulation is adopted to build the equilibrium equations of a beam element,the tangent stiffness matrix is derived from the principle of minimum potential energy,the computational procedure for large rotation is applied to compute new coordinates of elements and nodes,and the rigid displacement is taken away from the total displacement to get strain-producing deformations to obtain the precision increment of internal forces.Finally,two numerical examples were given to testify the correction and precision of this method.
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