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Applied Mathematics and Mechanics

, Volume 17, Issue 8, pp 789–794 | Cite as

A decomposition depended on directions for nonsingular linear transformation

  • Zhang Shenxue
Article
  • 27 Downloads

Abstract

In this paper, we give a decomposition depending on p(1≤p≤n−2) orthonormal directions assigned for nonsingular linear transformation F on a n-dimension (n≥3) Euclidean space En, and then prove that there exist q(q=n−p) quasi-principal directions for F depending on the preceding p orthonormal directions. As applicance of the preceding result, we derive that there exist at least two orthonormal principal directions of strain in arbitrary plane of body which is in homogeneous deformation, and strain energy density is function of 5 real numbers under arbitrary quasi-principal base for the preceding nonsingular linear transformation.

Key words

nonsingular linear transformation quasi-principal directions decomposition 

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References

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    Y. C.Chen, Stability of homogeneous deformations of an incompressible elastic body under dead-load surface tractions, J. Elasticity, 17 (1987), 223–248.Google Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • Zhang Shenxue
    • 1
  1. 1.Department of MathematicsJilin UniversityChangchunP. R. China

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