利用形函数性质产生直梁单元形函数的方法

journal6 ›› 2004, Vol. 25 ›› Issue (1): 22-25.

利用形函数性质产生直梁单元形函数的方法

( 1. 中南大学铁道校区土木建筑学院, 湖南长沙410075; 2. 湖南省高速公路管理局, 湖南长沙410000）

出版日期:2004-03-15 发布日期:2012-11-06
作者简介:娄平( 1968-) , 男, 湖南省浏阳县人, 博士, 中南大学土木建筑学院讲师, 主要从事列车轨道( 桥梁) 振动研究.
基金资助:
国家自然科学基金资助项目( 50078006)

A Method for Generating Straight Beam Element Shape Functions by Means of Its Properties

( 1. School of Civil Engineering & Architecture, Railway Campus, Central South University, Changsha 410075, Hunan China;2. High- speed Highway Administration Bureau of Hunan Province, Changsha 410000, China)

Online:2004-03-15 Published:2012-11-06

摘要/Abstract

摘要：利用形函数性质产生直梁单元形函数: 首先利用直梁单元形函数在其余节点上的性质构造在第j 个节点上包含待定常数的形函数表达式, 然后利用该形函数在第j 个节点上的性质, 求得在该节点上的所有形函数, 最后重复上述步骤可得到梁单元其余节点上的形函数. 以3 节点6 自由度直梁单元为例, 阐述了该方法产生形函数的应用, 同时也给出了2 节点6 自由度和2 节点8 自由度直梁单元的形函数. 与传统的方法相比, 该方法求解形函数的工作量显著减少.

关键词： 形函数, 直梁单元, Hermitian多项式

Abstract: A method for generating straight beam element shape functions by means of its propert ies is presented. The procedures for generating straight beam element shape function are following. Firstly, the shape functions with unknown constants at j th node in beam element are constructed by means of the properties of the shape function in remaining nodes in the same element; Secondly, the shape functions at the j th node are obtained by using the properties of this shape function at j th node; Lastly, the above steps are repeated, and then the functions at other node are found. The approach is illustrated by generating shape functions of three- node straight beam element with six degrees of freedom.The shape funct ions of two- node straight beam element with six degrees of freedom and two- node straight beam element with eight degrees of freedom are given. Compared with the classical method, the proposed method decreases the amount of work for solving shape functions obviously.

Key words: shape functions, straight beam element, Hermitian polynomials

娄平, 郑祖勇, 曾庆元. 利用形函数性质产生直梁单元形函数的方法[J]. journal6, 2004, 25(1): 22-25.

LOU Ping, ZHENG Zu-Yong, ZENG Qing-Yuan. A Method for Generating Straight Beam Element Shape Functions by Means of Its Properties[J]. journal6, 2004, 25(1): 22-25.