空间薄壁截面梁的材料非线性有限元模型

A MATERIAL NONLINEAR FINITE ELEMENT MODEL OF SPATIAL THIN-WALLED BEAMS

  • 摘要: 根据Bernoulli-Euler梁理论和Vlasov薄壁杆件理论,通过设置单元内部节点和对弯曲转角和翘曲角采取独立插值的方法,建立了可考虑剪切变形,弯扭耦合,约束扭转和二次剪应力引起的翘曲的空间薄壁截面梁的材料非线性有限元模型。假定材料为理想塑性体,符合Von Mises屈服准则和Prandtle-Reuss增量关系,采用有限分割的方法,在单元长度和截面上取一定数量的高斯点,然后进行数值积分得到空间薄壁截面梁的弹塑性刚度矩阵。算例表明该文所建模型具有较好的精度,适用于可用空间薄壁截面梁模型分析的薄壁结构。

     

    Abstract: Based on the theories of Bernoulli-Euler beams and Vlasov’s thin-walled members, a new material nonlinear finite element model is developed by adding an interior node to the element and applying the independent interpolation to bending angles and warp. Factors such as shear deformation, coupling of flexure and torsion and warp induced by non-uniform torsion and second shear stress are all considered in this model. Material of the element is assumed to be perfectly plastic, complying with Von Mises’ yielding rule and the incremental relationship of Prandtle-Reuss. With the aid of the finite segment method, a certain amount of Guass points are distributed along the length of the element and in its cross section, thus the elastoplastic stiffness matrix being derived by numeric integration. Examples testify to the precision and validity of the model. It concludes that the model is applicable to the analysis of thin-walled structures.

     

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