Engineering Mechanics ›› 2006, Vol. 23 ›› Issue (10): 45-48.

• 基本方法 • Previous Articles     Next Articles

APPLICATION OF LACONIC NOTATIONS IN FORMULA DERIVATION AND CALCULATION OF COMPONENTS IN TENSOR ANALYSIS

SHI Jiao1, WANG Zheng-zhong1, CAI Kun2   

  1. 1. College of Water Resourses and Architectural Engineering, Northwest A&F University, Yangling 712100, China;2. Department of Engineering Mechanics, Dalian University of Technology, Dalian 116023, China
  • Received:2005-01-11 Revised:2005-08-21 Online:2006-10-25 Published:2006-10-25

Abstract: Tensor analysis plays an important role in computational mechanics. Due to its complexity, the theory is hard to be accepted and applied conveniently. To solve this problem, laconic notations for tensors are presented here to simplify formula derivation in tensor analysis. These notations are different from traditional ones of tensors. They are similar to arrays used in Fortran routine or commercial software Matlab. Laconic notations for the operations of tensors such as dyadic product, inner product and transposition etc. are given, respectively. By this method, one can derive formula easily and accurately. Another point in this work is that a simple method of obtaining the components of a fourth-order tensor is presented by introducing the concept of vectorization of matrix. It makes the components of high-order tensors to be visual and straightforward for symbolic operation and numerical calculation. The theory of tensor analysis will be easy to master if one grasps these two points of this article.

Key words: tensor analysis, dyadic product, laconic notation, vectorization of matrix, component of a tensor

CLC Number: 

  • O151.24
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