[1]兑关锁,谢玉树.极分解中转动张量的计算及近似分析[J].南京理工大学学报(自然科学版),1998,(01):90-93.
 Dui Guansuo Xie Yushu.The Computation and Approximate Analysis on the Rotation Tensor in the Polar Decomposition[J].Journal of Nanjing University of Science and Technology,1998,(01):90-93.
点击复制

极分解中转动张量的计算及近似分析()
分享到:

《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

卷:
期数:
1998年01期
页码:
90-93
栏目:
出版日期:
1998-02-28

文章信息/Info

Title:
The Computation and Approximate Analysis on the Rotation Tensor in the Polar Decomposition
作者:
兑关锁谢玉树
南京理工大学理学院, 南京210094
Author(s):
Dui Guansuo Xie Yushu
School of Sciences, NUST, Nanjing 210094
关键词:
连续介质力学 张量 近似计算
Keywords:
cont inuum mechanics tenso rs appr oximate computat ion
分类号:
O33
摘要:
该文利用Cayley-Hamilton定理给出了转动张量R的显式表示,其中只包含变形梯度F的较低次幂及U和F的主不变量,由此获得了转动角的计算公式和转动轴的显式表达。最后通过近似分析,给出了在小变形中等转动情况下转动张量和伸长张量的近似表示。
Abstract:
By use of Cayley- Hamilton theorem, a representat ion for the rotation tensor w hich contains the low er pow ers o f deformat io n g radient is pr opo sed . An ex plicit fo rmula of rotat ion ang le is der iv ed and a representat io n for the ro tat ion tensor ax is is obtained. Final ly, thro ug h the appr ox imate analysis, the appro ximate r epresentat ion on the rotat ion tenso r and st retch tensor is proposed.

参考文献/References:

1 Mart ins L C, Siv eir a R F, Podio-Guidugli P. On the v anishing o f the additiv e measures o f st rain and ro tation for finite deformations. J Ela s, 1987, 17: 189~193
2 Ho ger A, Carlson D E. Determinatio n of the st retch and ro tation in the po lar decompo sitio n of the deformatio n gr adient . Quart Appl M ath, 1984, 42: 113~117
3 T ing T C T. Determ inatio n o f C 1/2 and C- 1/ 2 mor e general iso tro pic t enso r functions of C. JElas , 1985, 15: 319~385
4 Saw y ers K. Comm ents o n t he paper “Determination of t he str etch and r ota tio n in t he po lar decompo sitio n o f t he defo rma tio n gr adient ”by A Ho ger and D E Carlson. Quart Appl Math, 1986, 44: 309~311
5 Xiong Z H, Zheng Q S. Gener al algo rithms fo r the po lar decompo sitio n and str ain. Act a Mechanica Sinica, 1988, 4: 175~181
6 Rivlin R S. Fur ther r emarks on the stress-deformation r elatio ns for iso tr opic mat erials. J Ratio nal M ech Anal, 1995, 4: 681~702
7 Nag hdi P M , Vongsar npigo on L. Small st rain accompanied by mo der ate r otat ion. Ar ch Rational Mech Anal, 1982, 80: 263~294
8 De Tommasi D, Mar zano M. Small str ain and moderat e r ot atio n. J Elas, 1993, 32: 37~50

相似文献/References:

[1]兑关锁.两类张量方程解的新表示[J].南京理工大学学报(自然科学版),1998,(06):561.
 Dui Guansuo.Some New Representations for Solutions of Two Kinds of Tensor Equations[J].Journal of Nanjing University of Science and Technology,1998,(01):561.
[2]刘隆德.广义相对论的三大验证[J].南京理工大学学报(自然科学版),1981,(02):94.

备注/Memo

备注/Memo:
兑关锁 男 34岁 工程师
更新日期/Last Update: 2013-03-29