开口薄壁杆件结构稳定分析的精确单元和两步求解算法  

An exact finite element and a two-step algorithm for stability analysis of frame structures with open thin-walled sections

作　　者：李文雄[1,2] 马海涛[1] 高兴军[1] 

机构地区：[1]华南理工大学土木工程系亚热带建筑国家重点实验室,广州510640 [2]华南农业大学水利与土木工程学院,广州510642

出　　处：《计算力学学报》2012年第3期405-411,共7页Chinese Journal of Computational Mechanics

基　　金：华南理工大学亚热带建筑科学国家重点实验室自主研究课题项目

摘　　要：从控制微分方程的通解出发,构造受偏心压力作用开口薄壁杆件的精确形函数,建立用于开口薄壁杆件结构稳定性分析的精确有限元,得到了单元刚度矩阵和几何刚度矩阵的显式表达,提出了计算给定区间内各阶临界荷载以及相应失稳模态的两步计算方法。计算结果表明,与常规单元相比,采用精确单元无需进行网格细分就可以获得精确的数值结果,结合本文的两步求解算法,可以准确获得给定区间内全部临界荷载和失稳模态。Based on general solutions of the homogeneous governing equation for the stability analysis of thin-walled member with open section under eccentric axial load,new shape functions are constructed and a new finite element is formulated. The explicit expressions of element stiffness matrix and geometric stiffness matrix are derived. A two-step algorithm is proposed for stability analysis of thin-walled struc- tures. The numerical examples are presented, confirming that exact solutions can be obtained even when each member is modeled with one element. All the critical loads and buckling modes in a given range can be determined with the proposed two-step algorithm.

关 键 词：有限元法 薄壁杆件 稳定分析 刚度矩阵 精确单元 

分 类 号：O343[理学—固体力学]