悬臂梁静态几何非线性的有限元分析

Finite Element Analysis of Static Geometry Nonlinear about Cantilever Beam

摘要: 介绍了悬臂梁几何非线性的有限元模型，并对悬臂梁的应力应变关系进行了推导(在线性范围内)，在此基础上，利用有限元分析软件，对悬臂梁结构的静态几何非线性进行了有限元分析，研究发现，当悬臂梁结构在受到大变形而出现几何非线性时，现有的应力应变关系不再呈线性关系，而是呈现非线性，其理论推导必须采用非线性方程组来计算，而非线性方程组的求解可采用大变形问题的增量法——T.L法(拉格朗日法)。

Abstract: The finite element model of geometry nonlinearity about cantilever has been introduced in this paper. The relation of strain-stress about cantilever has been deduced (in range of linearity). Based on this, using finite element analysis soft, the static geometry nonlinearity of cantilever beam structure has been finitely analyzed. The study finds that the existing strain-stress relation is not linear relation when the cantilever beam structure shows the geometry nonlinearity after receiving large deformation, but is nonlinearity, and that the theoretical derivation must be computed by using nonlinear system of equations. But the solution of nonlinear equations can use increment means of large distortion question, which is T.L means (Lagrange means).