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Applied Mathematics and Mechanics

, Volume 8, Issue 10, pp 991–1002 | Cite as

On the structure of continua and the mathematical properties of algebraic elastodynamic of a triclinic structural system

  • Gu An-hai
Article

Abstract

This paper is neither laudatory nor derogatory but it simply contrasts with what might be called elastostatic (or static topology), a proposition of the famous six equations. The extension strains and the shearing strains
which were derived by A.L. Cauchy, are linearly expressed in terms of nine partial derivatives of the displacement function (u i ,u j ,u h )=u(x i ,x j ,x k ) and it is impossible for the inverse proposition to sep up a system of the above six equations in expressing the nine components of matrix ((u i ,u j ,u h )/(x i ,x j ,x k )). This is due to the fact that our geometrical representations of deformation at a given point are as yet incomplete[1]. On the other hand, in more geometrical language this theorem is not true to any triangle, except orthogonal, for “squared length” in space[2].

The purpose of this paper is to describe some mathematic laws of algebraic elastodynamics and the relationships between the above-mentioned important questions.

Keywords

Vector Space Banach Algebra Projective Group Mathematical Property Projective Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Shanghai University of Technology (SUT) 1987

Authors and Affiliations

  • Gu An-hai
    • 1
  1. 1.Zhengzhou Aluminum PlantZhengzhou

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