双层弹性支承梁的有限元分析  

Finite element analysis of two-layered beam resting on elastic supports

作　　者：娄平[1] 曾庆元[1] 郑祖勇[2] 

机构地区：[1]中南大学土木建筑学院,湖南长沙410075 [2]湖南省高速公路管理局,湖南长沙410000

出　　处：《湘潭矿业学院学报》2004年第1期27-30,共4页Journal of Xiangtan Mining Institute

基　　金：国家自然科学基金项目(编号:50078006);铁道部科技研究开发计划项目(编号:2001G029);教育部博士点基金项目(编号:20010533004)

摘　　要：用有限单元法分析了双层弹性支承梁的静力响应.双层弹性支承梁结构由二种平行的梁(上层梁和下层梁)、上层梁和下层梁之间的离散弹簧和下层梁下部的Winkler基础组成.上层长梁、下层短梁、离散弹簧、Winkler基础和作用在上层梁上的荷载视为一个系统,并将该系统进行有限单元离散,梁单元的弯曲形函数采用Hermitian3次方插值函数,利用变分原理及形成矩阵的"对号入座"法则建立该系统有限单元形式的平衡方程.阐明了单元刚度矩阵以及在上层梁单元作用竖向集中荷载或分布荷载下单元节点荷载列阵的形成.举例说明了该方法的应用,为类似结构的力学分析提供了一种数值方法.图5,参13.A finite element method is applied to analyze the static response of structure of two-layered beam resting on elastic supports.This structure is composed of two kinds parallel beams named as the upper beam and the lower beams in the paper,discrete springs between the upper beam and the lower beams,and Winkler foundation under the lower beams.Firstly,upper long beam,lower short beams,discrete spring,Winkler foundations and loads acting on the upper beam are considered as an entire system.Then,the system is separated into a number of finite elements and Hermitian cubic interpolation functions are utilized as the bending shape functions of the two-node beam element.At last,the system of equilibrium equations may be established in finite element form by using variational principle and the 'Set-in-right-position' rule for formulating matrixes.The formulation for element stiffness matrixs,and vectors of nodal of element with the upper beam element subjected to either vertical concentrated load or distributed loads is illustrated.An example is used to illustrate the proposed method. A numerical method is provided with resemblance structure.5figs,13refs.

关 键 词：有限单元 梁 结构分析 变分原理 HERMITIAN 3 次插值函数 刚度矩阵 

分 类 号：U213.242[交通运输工程—道路与铁道工程] TB121[理学—工程力学]