变截面梁有限元分析  

The finite element analysis of non-uniform beams

作　　者：王晓臣[1] 蒲军平[1] 

机构地区：[1]浙江工业大学建筑工程学院,浙江杭州310032

出　　处：《浙江工业大学学报》2008年第3期311-315,共5页Journal of Zhejiang University of Technology

摘　　要：针对工程结构中广泛应用的变截面构件,根据有限单元法基本原理,在假定变截面模式的基础上,推导了变截面平面梁单元的单元刚度矩阵.使用笔者所给的单元分析梁高呈线性变化及抛物线性变化的矩形截面梁,所得计算结果将更加逼近于精确解.笔者给出了一个变截面悬臂梁和简支梁算例,计算表明,若用通常的分段等刚度单元进行近似计算,必须使用较多的单元数才能趋近于精确解,运用该方法可以使变截面梁的分析大大简化.The stiffness matrix of a plane non-uniform beam was deduced to analyze the non-uniform members used increasingly in engineering structures based on the basic principles of finite element method and assuming the mode of non-uniform section. The non-uniform rectangular beams with both linear and parabolic variation heights of the transverse section were analyzed by use of given elements. It was showed that the results were more approach to the exact solutions. A non-uniform cantilever beam and a non-uniform simple supported beam were presented as an example, and the calculation results showed that, if segmental uniform finite elements were employed, more elements must be required to approach the current exact solution. So the present elements can apparently simplify the analysis of non-uniform beams.

关 键 词：变截面梁 梁单元 刚度矩阵 有限单元法 

分 类 号：O242.21[理学—计算数学]