构造弹性力学位移函数的机械化算法<sup>*</sup>

张鸿庆; 冯红

构造弹性力学位移函数的机械化算法^*

张鸿庆,
冯红

大连理工大学数学研究所 116023

基金项目: * 国家自然科学基金;数学机械化研究中心资助

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出版历程
- 收稿日期: 1994-04-25
- 刊出日期: 1995-04-15

The Mechanical Method of Constructing the Displacement Functions in Elasticity

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

摘要

摘要: 本文证明线性算子方程组Au=f的一般解为u=Cv+e,其中v满足方程组Dv=g,D是对角矩阵。以Hilbert零点定理的构造性证明为基础,给出了C,D,e的机械化求示。用此方法可以给出各种弹性力学位移函数的机械化算法。
- 弹性力学 /
- 位移函数 /
- 机械化算法 /
- Hilbert零点定理
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

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参考文献(12)

[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).