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基于传统欧拉直梁力学模型,对初始扭转欧拉梁有限元模型进行系统的分析与研究。采用2节点12个自由度模型,单元轴向位移插值函数采用2节点拉格朗日插值函数,梁截面横向弯曲位移u,v仍采用三次式位移模式。绕梁轴扭转角位移函数φz同轴向位移函数一样采用2节点拉格朗日插值函数。首先基于作者先前文献中初始扭转梁的弯曲正应变关系,导出初始扭转欧拉梁单元刚度矩阵。最后,通过矩形截面初始扭转悬臂梁算例,并与ANSYS三维实体有限元分析结果进行对比分析,表明建立的初始扭转欧拉梁单元刚度矩阵具有良好的精度。
Based on the traditional Euler beam mechanical model, the initial torsional Euler beam finite element model is systematically analyzed and studied. Adopting 12-degree-of-freedom model of 2-node model, the displacement function of axial displacement of unit adopts Lagrange interpolation function of two nodes, and the lateral bending displacement u and v of beam cross-section still adopts cubic displacement mode. Around the beam axis torsion angle displacement function φz coaxial displacement function using the same 2-node Lagrange interpolation function. First, the initial torsional Euler beam element stiffness matrix is derived based on the positive bending strain of the initial torsion beam in the author’s previous work. Finally, the initial torsion cantilever beam example with rectangular section was compared with the finite element analysis results of ANSYS. The results show that the established initial torsional Euler beam element stiffness matrix has good accuracy.