摘要
固定形状的单元位移插值函数不能合理地近似变截面梁内部的位移变化,从而影响了传统梁单元用于计算变截面梁的精度。采用直接基于单元平衡的思想给出了计算变截面梁反应的有限元方法,解决了单元位移插值函数局限性所带来的问题。导出了变截面梁单元的单元刚度矩阵、单元等效节点荷载和单元一致质量矩阵。在此基础上,利用编制的程序进行了算例验证与分析。算例验证了本文理论的正确性,表明本文方法具有很高的计算精度。
The element shape functions with fixed shapes cannot rationally approximate the deformation in a deformed beam with variable cross-section, which results in an inaccuracy of traditional beam elements. The paper presents a method to analyze beam with variable cross-section by using direct elementbased equilibrium framework. This method avoids the inaccuracy caused by the limitation of element shape functions. The stiffness matrix, equivalent nodal load and consistent mass matrix are derived for the beam element with variable cross-section. A computer program is then developed and a numerical example is provided to verify the presented method. It is shown that the theory is correct and the method has higher accuracy than the traditional beam elements.
出处
《计算力学学报》
EI
CAS
CSCD
北大核心
2009年第2期226-231,共6页
Chinese Journal of Computational Mechanics
基金
国家自然科学基金(90815014,90715021)
地震行业科研专项(200808073)资助项目
关键词
变截面梁
单元平街
等效节点荷载
一致质量矩阵
beam with variable cross-section
element equilibrium
equivalent nodal load
consistent mass matrix
