一种考虑截面任意变形模式梁的有限元模型

Finite element model of beem considering arbitrary deformation mode of cross-section

提出了一种考虑截面完整变形的截面插值梁模型,并用于机翼结构的建模与分析。首先引入截面插值函数——拉格朗日函数描述截面形状,以位移向量为未知变量描述截面位移,在此基础上依据插值理论构造梁单元位移场。不同于传统梁单元通过假定的中性轴的挠度和转角来确定梁截面各点位移,该梁模型摒弃了中性轴假设与平截面假设,通过截面插值函数得到梁截面面内、面外变形;然后通过有限元理论推导了梁单元刚度矩阵与质量矩阵;最后利用截面插值梁单元对机翼各部件进行有限元建模,并展开典型工况下的静力学分析以及动力学分析,与Nastran实体单元计算结果进行了对比分析,验证了该梁模型的有效性,为机翼的结构设计和强度分析提供了一种新的简化建模方法。

A cross-section interpolation beam model considering the complete deformation of the cross-section is proposed and used to model and analyze the wing structure.First,the Lagrange functions are introduced as the interpolation function to describe the shape of the beam crossection,and the displacement vectors are used as unknown variables to describe the displacement of the cross-section.On this basis,the displacement field of the beam element is constructed according to the interpolation theory.While the displacements of the beam in the conventional beam element are determined by the deflection and rotation of the assumed neutral axis,the new beam element rejects the neutral axis hypothesis and flat section hypothesis,and the deformation of the beam cross-section is obtained by the interpolation functions.Then based on the finite element theory,the stiffness matrix and the mass matrix of the beam element are derived.Finally,the wing components are modeled by the cross-section interpolation beam element,and the static analysis and dynamic analysis under typical conditions are carried out.The validity of the beam model is verified by comparing the result with the results of Nastran solid model,showing that the model provides a one-dimensional beam simplified modeling method for the structural design and strength analysis of the wing.