TY - JOUR
T1 - 连续介质力学教学之矢量张量运算的图形表示
AU - Yu, Yajun
AU - Huang, Yue
AU - Wu, Hua
AU - Deng, Zichen
N1 - Publisher Copyright:
© 2024 Chinese Academy of Mechanics. All rights reserved.
PY - 2024/8
Y1 - 2024/8
N2 - 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.
AB - 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.
KW - graphical notation
KW - pedagogy
KW - tensor analysis
KW - vector analysis
UR - http://www.scopus.com/inward/record.url?scp=85203083202&partnerID=8YFLogxK
U2 - 10.6052/1000-0879-24-002
DO - 10.6052/1000-0879-24-002
M3 - 文章
AN - SCOPUS:85203083202
SN - 1000-0879
VL - 46
SP - 883
EP - 887
JO - Mechanics in Engineering
JF - Mechanics in Engineering
IS - 4
ER -