用统一分析梁与有限节线法分析弹性薄壁截面构件  

Elastic Analysis of Arbitrary Thin-Walled Structural Members Based on the Unified Analytical Beam Model With the Finite Nodal Line Method

作　　者：龚耀清[1] 孙博[1] 陈晓东[1] 

机构地区：[1]河南理工大学土木工程学院,河南焦作454003

出　　处：《应用数学和力学》2015年第4期352-361,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(51178164);河南省重点学科资助项目(62705/004)~~

摘　　要：传统薄壁截面梁理论不仅与梁的长细比有关,还强烈地依赖于其横截面的形状和荷载的作用方式.为了解决任意长细比、任意形状弹性薄壁截面杆状类结构构件或结构体系受任意荷载作用的力学分析问题,提出了一种新的梁模型——统一分析梁,一种结构数值分析新方法——有限节线法.利用统一分析梁模型和有限节线法不仅可以分析任意弹性薄壁杆状类结构构件的力学行为,而且当问题的性质与传统梁理论的前提条件一致时,会得出同样精度的解答.算例计算结果证明了统一分析梁的合理性与有限节线法的正确性.The traditional thin-walled beam theory is strongly dependent on the slenderness ra- tio, the shape of its cross section and the load form of a beam. In order to investigate the elastic behaviors of arbitrary thin-walled beams under arbitrary loads, a unified analytical model for all thin-walled structural members, named ＇unified analytical beam＇ （UAB）, and a novel compu- tational methodology titled ＇ f＇mite nodal line method＇ （FNLM） were presented. By means of UAB and FNLM, the elastic analysis of arbitrary thin-walled structural members can be conven- iently carried out. Furthermore, when the properties of a beam problem are consistent with the application conditions for the traditional beam theory, an equal-precision solution to the prob- lem will be obtained with both the FNLM and the traditional one. The computational comparison through several beam examples verifies the rationality and correctness of the proposed UAB and FNLM.

关 键 词：薄壁截面梁 传统梁理论 统一分析梁 有限节线法 非均匀扭转 

分 类 号：O341[理学—固体力学] TB301[理学—力学]