连续介质力学教学之矢量张量运算的图形表示  

VECTOR TENSOR GRAPHICAL NOTATION FOR CONTINUUM MECHANICS TEACHING

作　　者：尉亚军 黄玥 吴华 邓子辰[1] YU Yajun;HUANG Yue;WU Hua;DENG Zichen(School of Mechanics,Civil Engineering and Architecture,Northwestern Polytechnical University,Xi’an 710129,China)

机构地区：[1]西北工业大学力学与土木建筑学院,西安710129

出　　处：《力学与实践》2024年第4期883-887,共5页Mechanics in Engineering

基　　金：陕西省学位与研究生教育研究项目(SXGERC2023018);2023年度西北工业大学课程建设项目(PX-27232200)资助。

摘　　要：掌握矢量分析和张量分析基本知识是学习和研究连续介质力学的基础。本文介绍矢量分析和张量分析的图形表示法,包括矢量的点积、叉积、混合积、一阶微分、二阶微分以及二阶张量的迹、简单缩并、双缩并、散度等。根据图形表示法能快速证明常用矢量、张量等式,比数学推导法更直观、简洁、高效。图形表示法的引入以及与数学推导法的结合有助于深化学生对矢量分析和张量分析的理解,提升连续介质力学课堂教学的趣味性。Mastering basic knowledge of vector analysis and tensor analysis is the foundation for learning and studying continuum mechanics.In this paper,graphical notation for vector and tensor analysis is introduced,including vector’s dot product,cross product,triple product,first-order differential,second-order differential,trace of second-order tensor,tensor’s simple contraction,double contraction,divergence operator,etc.According to graphical notation,some vector and tensor equations can be proved quickly,which is more intuitive,concise and efficient than other mathematical derivations.The introduction of graphical notation and combination with mathematical derivation may deepen the understanding of vector analysis and tensor analysis for students,and enhance interest for continuum mechanics in teaching.

关 键 词：矢量分析 张量分析 图形表示 教学法 

分 类 号：O33[理学—一般力学与力学基础]