一类非对称各向同性张量函数导数的不变表示

王志乔; 兑关锁

一类非对称各向同性张量函数导数的不变表示

北京交通大学土建学院工程力学研究所,北京 100044

基金项目: 国家自然科学基金委员会、二滩水电开发有限责任公司雅砻江水电开发联合研究基金资助项目(50539030)

详细信息

作者简介:
王志乔(1978- ),男,河北人,博士;兑关锁(1963- ),男,河南人,副教授(联系人.Tel:+86-10-51688437;Fax:+86-10-51682094;E-mail:gsdui@center.njtu.edu.cn).

中图分类号: O331；O183.2
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出版历程
- 收稿日期: 2006-11-03
- 修回日期: 2007-03-30
- 刊出日期: 2007-09-15

Basis-Free Expressions for the Derivatives of a Subclass of Nonsymmetric Isotropic Tensor Functions

Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing 100044, P. R. China

摘要

摘要: 将Dui和Chen于2004年提出的求解对称各向同性张量函数导数的方法推广到一类满足可交换条件的非对称各向同性张量函数情况,此类函数比以往研究的更具一般性．在有3个不同特征根时,由可交换性引进张量函数相对应的标量函数,进而求得此类非对称各向同性张量函数及其导数的不变表示形式．在2或3重特征根时,利用求极限的办法给出此类张量函数及其导数的表示形式．
- 非对称张量 /
- 张量函数导数 /
- 标量函数 /
- 四阶张量
Abstract: The method for solving the derivatives of symmetric isotropic tensor-valued functions proposed by Dui and Chen was generalized to a sub-class of nonsymmetric tensor functions satisfying the commutative condition. This subclass of tensor functions is more general than those investigated by the existing methods. In the case of three distinct eigenvalues, the commutativity makes it possible to introduce two scalar functions, which will be used to construct the general nonsymmetric tensor functions and their derivatives. In the cases of repeated eigenvalues, the results are acquired by taking limits.
- nonsymmetric tensor /
- derivative of tensor function /
- scalar function /
- fourth-order tensor

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参考文献(18)

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一类非对称各向同性张量函数导数的不变表示

作者简介:
王志乔(1978- ),男,河北人,博士;兑关锁(1963- ),男,河南人,副教授(联系人.Tel:+86-10-51688437;Fax:+86-10-51682094;E-mail:gsdui@center.njtu.edu.cn).

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Basis-Free Expressions for the Derivatives of a Subclass of Nonsymmetric Isotropic Tensor Functions

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一类非对称各向同性张量函数导数的不变表示

作者简介: 王志乔(1978- ),男,河北人,博士;兑关锁(1963- ),男,河南人,副教授(联系人.Tel:+86-10-51688437;Fax:+86-10-51682094;E-mail:gsdui@center.njtu.edu.cn).

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出版历程

Basis-Free Expressions for the Derivatives of a Subclass of Nonsymmetric Isotropic Tensor Functions

计量

出版历程

目录

作者简介:
王志乔(1978- ),男,河北人,博士;兑关锁(1963- ),男,河南人,副教授(联系人.Tel:+86-10-51688437;Fax:+86-10-51682094;E-mail:gsdui@center.njtu.edu.cn).