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.
Abstract
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.
基金项目
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)
NETL
NSTL
万方数据