IMPLEMENTATION OF CONSISTENT UPDATED LAGRANGIAN FORMULATION FOR STATIC ANALYSIS OF GEOMETRICALLY NONLINEAR BEAM
IMPLEMENTATION OF CONSISTENT UPDATED LAGRANGIAN FORMULATION FOR STATIC ANALYSIS OF GEOMETRICALLY NONLINEAR BEAM
复制标题
几何非线性梁静态分析的一致更新拉格朗日公式的实现
DOI：
10.1139/tcsme-2000-0009
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发表时间：
2000
影响因子：
0.9
通讯作者：
W. Cleghorn
中科院分区：
文献类型：
--
作者：
A. Misra;K. Behdinan;W. Cleghorn
本文将用于求解大位移非线性问题的一致更新拉格朗日（CUL）公式与全拉格朗日（TL）公式和更新拉格朗日（UL）公式进行了比较。这种比较表明，这些公式使用不同的参考配置开发刚度和内部负载矢量，但产生相同的条款。通过使用连续介质力学方法建立CUL公式的控制平衡方程，证实了三种拉格朗日公式的等效性。针对一个两节点、二维、大位移、小应变的Euler-Bemoulli梁单元，建立了平衡方程的CUL有限元列式，以说明获得刚度矩阵和内载荷向量的过程。所有三个有限元拉格朗日公式的实施和测试的静态分析的二维，欧拉-Bemoulli直悬臂梁进行横向尖端载荷在t.
In this paper, the consistent updated Lagrangian (CUL) formulation used for solving large-displacement non-linear problems is compared with the total Lagrangian (TL) and the updated Lagrangian (UL) formulations. This comparison indicates that these formulations use different reference configurations for developing stiffness and internal load vectors but yield identical terms. The equivalence of the three Lagrangian formulations was confirmed by developing the governing equilibrium equations for the CUL formulation using the continuum mechanics approach. For a two-noded, two-dimensional, large displacement-small strain Euler-Bemoulli beam element, the CUL finite element formulation of the equilibrium equations was developed to illustrate the procedure used to obtain the stiffness matrix and internal load vectors. All three finite element Lagrangian formulations were implemented and tested for static analysis of two-dimensional, Euler-Bemoulli straight cantilever beam subjected to a transverse tip load at t...