基于MATLAB的变截面梁单元有限元分析

摘要

变截面梁在工程实践中被广泛应用.给出常用的梁高呈线性变化及抛物线性变化的矩形截面梁单元,根据有限元基本原理,借助于MATLAB强大的符号运算功能建立该类变截面梁单元的刚度矩阵,并给出一个变截面悬臂梁的算例,所得结果更加逼近于精确解.结果表明运用该方法可以使变截面梁的分析大大简化.%The non-uniform beam is widely used in engineering practice. This paper presents the commonly used non-uniform rectangular beam element with both linear and parabolic variation heights of the transverse section. Based on the basic principle of finite element method, by means of MATLAB powerful symbolic operation, it is convenient to establish its stiffness matrix. A non-uniform cantilever beam is presented as an example, which show that the results are more accurate solutions and the present elements can apparently simplify the analysis of non-uniform beams.