Mathematica在Winkler地基梁分析中的应用

Application of Mathematica in the Analysis of Winkler Foundation Beam

Winkler地基梁挠曲方程的分析涉及高阶微分方程的求解,从而使得手工进行该项工作既耗时又枯燥。为提高本科生Winkler地基梁的分析水平,在土木工程本科教学中引入Mathematica软件。将作用在Winkler地基梁上的均布荷载、集中力和集中力偶用不同类型的奇异函数在软件中统一表达,借助软件强大的计算能力,对两个算例进行分析计算及内力曲线绘制。两个算例证明Mathematica的引入有利于学生对自己感兴趣的具体边界条件下的探索性问题运用Winkler理论进行分析。

The analysis of the deflection equation of Winkler foundation beam involves the solving of a higher-order differential equation,which makes this work by hand time-consuming and boring.In order to improve the undergraduates’analysis level of Winkler foundation beam,Mathematica software is introduced in the undergraduate teaching of civil engineering.Uniform loads,concentrated loads and concentrated moments acting on the beam are uniformly expressed in the software by different types of singular functions.With the help of the powerful calculating capacity of the software,two examples are analyzed and calculated,and the internal force curves are drawn.Two examples show that the introduction of Mathematica is helpful for students to analyze the exploratory problems by using Winkler theory under specific boundary conditions that they are interested in.