VECTOR TENSOR GRAPHICAL NOTATION FOR CONTINUUM MECHANICS TEACHING


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, firstorder differential, secondorder differential, trace of secondorder 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.

