On the structure of continua and the mathematical properties of algebraic elastodynamic of a triclinic structural system
- 14 Downloads
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. On the other hand, in more geometrical language this theorem is not true to any triangle, except orthogonal, for “squared length” in space.
The purpose of this paper is to describe some mathematic laws of algebraic elastodynamics and the relationships between the above-mentioned important questions.
KeywordsVector 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.
Unable to display preview. Download preview PDF.
- Filonncko-Borodich, M.,Theory of Elasticity, Foreign Languages Publishing House, Moscow, 30–48.Google Scholar
- Gruenbory, K.W. and A.J. Weir,Linear Geometry, Springer-Verlag, New York-Heidelber Berlin (1977), 15–129.Google Scholar
- Konishi, Eiichi, etc.,Linear Algebra and Vectors Analysis (from Japanese), Liaoning Peo Publishing House, Shenyang, China (1981), 119. (Chinese version)Google Scholar
- Su Bu-qing,Affine Differential Geometry, Science Press, Beijing (1982), 19. (in Chinese)Google Scholar
- Compiling group of Mathematic Handbook,Mathematic Handbook, People’s Education Publishing House, Beijing (1980), 449. (in Chinese)Google Scholar
- Chien Wei-zang and Yeh Kai-yuan,Theory of Elasticity, Science Press, Beijing (1980), 63–64. (in Chinese)Google Scholar
- Kilechevski, I.A.,Elementary Tensor Operation and Its Application in Mechanics, People Education Publishing House, Beijing, China (1959), 27–33. (Chinese version)Google Scholar
© Shanghai University of Technology (SUT) 1987