The Mechanical Method of Constructing the Displacement Functions in Elasticity

Zhang Hong-qing; Feng Hong

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1995 > 16(4): 315-322

Zhang Hong-qing, Feng Hong. The Mechanical Method of Constructing the Displacement Functions in Elasticity[J]. Applied Mathematics and Mechanics, 1995, 16(4): 315-322.

Citation:

Zhang Hong-qing, Feng Hong. The Mechanical Method of Constructing the Displacement Functions in Elasticity[J]. Applied Mathematics and Mechanics, 1995, 16(4): 315-322.

Citation:

Zhang Hong-qing, Feng Hong. The Mechanical Method of Constructing the Displacement Functions in Elasticity[J]. Applied Mathematics and Mechanics, 1995, 16(4): 315-322.

PDF( 463 KB)

The Mechanical Method of Constructing the Displacement Functions in Elasticity

Institute of Mathematical Science, Dalian Univ. of Tech., Dalian, 116023

Received Date: 1994-04-25
Publish Date: 1995-04-15

Abstract

Abstract

In this paper we have proven the general solution to the equations of linear operators Au=f as u=Cv+e. where v satisfies the equation Dv=g and D is adiagonal matrix. Basing on the consstructive proof of Hilbert Nullstellensatz. we hare given the mechanical method of constucting C. D and e, and some of the mechanical algorithm displacement functions in elasticity are given by this method also.
- elasticity,
- displacement function,
- mechanical algorithm,
- Hilbert nullstellensatz

FullText(HTML)

References(12)

References

[1]	Gurtin, M. E., The linear theory of elasticity, Handbuck Der Physik Encyclopedia of Physics, Band Vla/2, Springer-Verlag, Berlin (1972).
[2]	王敏中,弹性力学通解和应力函数研究概况,力学进展.19(1) (1989), 65-72.
[3]	张鸿庆,弹性力学方程组一般解的统一理论.大连工学院学报,3 (1978), 23-47
[4]	张鸿庆,线性算子方程组一般解的代数结构.力学学报特刊(1981), 152-161.
[5]	Zhang Hong-qing and Feng Hong, Mechanical method for algebraic structure of the general solution to the system of linear operator equations, Proceedings of the 1992 International Workshop Mathematics Mechanisation, International Academic, Beijing(1992), 276-280.
[6]	Zhang Hong-qing and Wu Fang-xiang, Mechanical method to construct the general solution for a system of partial equation, Proceedings of the 1992 International Workshop Mathematiics Mechanisation, International Academic, Beijing(1992), 280-285.
[7]	吴文俊,《几何定理机器证明的基本原理》(初等几何部分),科学出版社(1984),
[8]	张鸿庆、杨光,变系数偏微分方程组一般解的构造,应用数学和力学,12(2) (1991),135-139.
[9]	胡海昌,横观各向同性体的弹性力学的空间间题,物理学报,9(2) (1953).
[10]	Youla, Dante.C.,Notes on n-dimensional system, Theory IEEE Transactions Circuits and Systems, Cas-31(6)(1984),105-111.
[11]	北京大学,《高等代数》,高等教育出版社(1988).
[12]	Jacobson, Nathan, Basic Algebra, W.H.Freeman and Company,San Francisco(1971).