摘 要：针对材料力学梁的弯曲问题，应用奇异函数法，将不连续的载荷写成统一的载荷函数，通过积分和代入边界条件求解剪力、弯矩、转角和挠度，并通过多个实例的计算进行验证。在详细阐述奇异函数法演算过程的基础上，应用 Mathematica实现了奇异函数法算法，并绘制了弯曲问题的剪力、弯矩、转角和挠度等图形。Mathematica 程序加以适当扩展，能够解决材料力学中各类问题的计算，对提高材料力学的教学能力和教学研究有着一定参考意义。
关键词：材料力学；奇异函数法；Mathematica；弯曲问题
DOI:10.19850/j.cnki.2096-4706.2022.011.030
课题项目：省级线上课程 (2020mooc483)；黄山学院校级教研项目 (2020JXYJ46)；校级“金课”工程力学 (2021JKXM10)；新工科背景下《材料力学》课程教学改革与探索——以智能制造专业为例 (2021JXYJ38)
中图分类号：TP39 文献标识码：A 文章编号：2096-4706（2022）11-0117-06
Application of Mathematica in Bending Problems of Material Mechanics
CAO Jianhua, GUO Dongxu
(Huangshan University, Huangshan 245041, China)
Abstract: Aiming at the bending problem of beams in the Material Mechanics, the singular function method is applied to write the discontinuous load as a uniform load function. The shear force, bending moment, rotation angle and deflection are solved by integrating and substituting the boundary conditions, and it is verified by the calculation of multiple instances. On the basis of elaborating the calculation process of the singular function method, the algorithm of the singular function method is realized by using Mathematica, and plots the graphs such as shear force, bending moment, rotation angle and deflection of the bending problems. The Mathematica program can be appropriately extended to solve the calculation of various problems in Material Mechanics, which has certain reference significance for improving the teaching ability and teaching research of the Material Mechanics.
Keywords: Material Mechanics; singular function method; Mathematica; bending problem
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作者简介：曹建华 (1983—)，男，汉族，江西九江人，讲师，博士，研究方向：力学教育、管道振动。