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基于传统薄壁直梁力学模型,对初始扭转薄壁梁有限元数值模型进行系统的分析与研究。首先基于初始扭转梁的几何变形微分关系,导出初始扭转薄壁梁圣维南翘曲应变。根据传统薄壁直梁有限元力学模型,考虑初始扭转梁圣维南翘曲变形,建立其有限元单元刚度矩阵。最后,通过椭圆截面初始扭转梁算例,并与ANSYS三维实体有限元分析结果进行对比分析,表明建立的考虑圣维南翘曲变形的初始扭转薄壁梁单元刚度矩阵具有良好的精度。
Based on the traditional thin-walled straight beam mechanical model, the finite element numerical model of the initial reversed thin-walled beam is systematically analyzed and studied. First, based on the differential geometry of the initial torsion beam, the strain of Saint-Venant warp in the initial reversed thin-walled beam is derived. According to the traditional finite element mechanics model of thin-walled straight beam, the initial torsion beam Sheng-nanan warpage is considered, and the stiffness matrix of the finite element element is established. Finally, the initial torsion beam elliptical cross-section example is compared with the ANSYS three-dimensional solid finite element analysis results show that the established initial stiffness of the torsion thin-walled beam considering Saint-Venant warping deformation has good accuracy.