On the Structure of Continua and the Mathematical Properties of Algebraic Elastodynamic of a Triclinic Structural System

Gu An-hai

Volume 8 Issue 10

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Article Navigation > Applied Mathematics and Mechanics > 1987 > 8(10): 931-941

Gu An-hai. On the Structure of Continua and the Mathematical Properties of Algebraic Elastodynamic of a Triclinic Structural System[J]. Applied Mathematics and Mechanics, 1987, 8(10): 931-941.

Citation:

Gu An-hai. On the Structure of Continua and the Mathematical Properties of Algebraic Elastodynamic of a Triclinic Structural System[J]. Applied Mathematics and Mechanics, 1987, 8(10): 931-941.

Citation:

Gu An-hai. On the Structure of Continua and the Mathematical Properties of Algebraic Elastodynamic of a Triclinic Structural System[J]. Applied Mathematics and Mechanics, 1987, 8(10): 931-941.

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On the Structure of Continua and the Mathematical Properties of Algebraic Elastodynamic of a Triclinic Structural System

Gu An-hai

Zhengzhou Aluminum Plant, Zhengzhou

Received Date: 1986-01-06
Publish Date: 1987-10-15

Abstract

Abstract

This paper is neither laudatory nor derogatory but it simply contrasts with what might be called elastosiatic (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_k) =u(xⁱ, 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_k)/∂(xⁱ, 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.

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References(8)

References

[1]	Filonneko-Borodich,M.,Theory of Elasticity,Foreign Languages Publishing House,Moscow,30-48.
[2]	Gruenbery,K.W.and A.J.Weir,Linear Geometry,Springer-Verlag,New York-Heidelberg-Berlin (1977),15-129.
[3]	小西荣一等著,《线性代数、向量分析》,辽宁人民出版社(1981), 119.
[4]	苏步青,《仿射微分几何学》,科学出版社(1982), 19.
[5]	谷安海,变换函数中Φ及KUR空间存在固定点的条件,应用数学和力学,7, 3 (1986), 273-277.
[6]	《数学手册》编写组,《数学手册》,人民教育出版社(1980), 449.
[7]	钱伟长、叶开沅,《弹性力学》,科学出版社(1980), 63-64.
[8]	Килъчевскйй И.А.,《张量计算初步及其力学上的应用》,人民教育出版社(1959), 27-33.

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