On Uniqueness, Existence and Objectivity of S-R Decomposition Theorem

Chen Mian; Liang Jingwei; Chen Xi; Chen Zhida

Volume 18 Issue 9

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1997 > 18(9): 763-768

WANG Xi-cheng, GE Zeng-jie, WU Hong-yu. An Algebraic Multigrid Method for Coupled Thermo-Hydro-Mechanical Problems[J]. Applied Mathematics and Mechanics, 2002, 23(12): 1307-1313.

Citation:

Chen Mian, Liang Jingwei, Chen Xi, Chen Zhida. On Uniqueness, Existence and Objectivity of S-R Decomposition Theorem[J]. Applied Mathematics and Mechanics, 1997, 18(9): 763-768.

WANG Xi-cheng, GE Zeng-jie, WU Hong-yu. An Algebraic Multigrid Method for Coupled Thermo-Hydro-Mechanical Problems[J]. Applied Mathematics and Mechanics, 2002, 23(12): 1307-1313.

Citation:

Chen Mian, Liang Jingwei, Chen Xi, Chen Zhida. On Uniqueness, Existence and Objectivity of S-R Decomposition Theorem[J]. Applied Mathematics and Mechanics, 1997, 18(9): 763-768.

PDF( 319 KB)

On Uniqueness, Existence and Objectivity of S-R Decomposition Theorem

1.
University of Petroleum, Beijing 102200, P. R. China;
2.
Chengdu Coal Mining Management Institute, Chengdu 610000, P. R. China;
3.
China University of Mining, Beijing 100083, P. R. China

Received Date: 1996-03-06
Publish Date: 1997-09-15

Abstract

Abstract

For a physically possible deformation field of a continuum, the deformationgradient function F can be decomposed into direct sum of a symmetric tensor S andan orthogonal tensor R. which is called S-R decomposition theorem. In this paper,the S-R decomposition unique existence theorem is proved. by employing matrix andtensor method. Also, a brief proof of its objectivity is given.
- S-R decomposition theorem,
- uniqueness,
- existence,
- objectivity

FullText(HTML)

References(4)

References

[1]	陈主达,《有理力学》,中国矿业大学出版社(1986),96-100.
[2]	陈勉,非线性连续体力学中的杆、壳大变形问题,中国矿业大学博士l论文(1991).
[3]	陈熙.有限变形和分解定理的存在性与唯一性,中国矿业大学硕士论文(1986).
[4]	Marvin Marcus and Henryk Minc,A Survey of Matrix Theory and Matrix Inequalities,Allyn and Bacon Inc.,Boston(1964),67.