有限变形问题拟主轴法<sup>*</sup>

有限变形问题拟主轴法^*

基金项目: * 国家教委优秀青年教师基金,国家杰出青年科学基金

Department of Engineering Mechanics, Qinghua University, Beijing 100084, P. R. China

摘要: 所谓拟主轴标架,是一个单位正交标架,且相对于该标架的剪应变分量很小。作为Hill的主轴法的一种实用推广,我们在拟主轴杯架下建立了应变、转动、旋率、应变率、共轭应力和应力率在拟主轴标架下的近似表示形式。发展拟主轴法的目的,是试图既保留主轴法的主要优点,又可作为某种分析大变形问题的高效数值示析方法的基础。
- 小剪切标架 /
- 拟主轴法 /
- 实用大变形方法
Abstract: A quasi-quasi-principal axis frame means a unit orthogonal frame in which the shear strains are small. As an extension of Hill's principal axis method we establish the approximate representations for various strains, the finite rotation tensor, spins, strain rates, conjugate stresses and their rates with respect to quasi-principal axes. The quasiprincipal axis method may function as a new basis of numerically analyzing finite deformation problems.
- small shear strain /
- quasi-principal axes /
- applied large deformation method

[1]	R.Hill,Aspects of invariance in solid mechanics,in Advances in Applied Mechanics,Vol.18 (Chia-Shun Yih,ed.),Academic Press,New York(1978),1-75.
[2]	R.Hill,Constitutive inequalities for isotropic elastic solids under finite strain,Proc.R.Soc.Lond.A314 (1970),457-472.
[3]	M.A.Biot,Mechanics of Incremental Deformation,John Wiley & Sons (1965).
[4]	郭仲衡、R,N,Dubey,非线性连续介质力学中的"主轴法",力学进展,13 (1983),1-17.
[5]	郭仲衡、梁浩云,从主轴法到抽象表示,力学进展,20 (1990),303-315.
[6]	梁浩云,主轴内蕴法与高维张量方程AX-XA=C,应用数学和力学,17(10) (1996),889-894.
[7]	郭仲衡,《非线性弹性理论》,科学出版社(1980).
[8]	A.Hoger and D.E.Carlson,Determination of the stretch and rotation in the polar decomposition of the deformation gradient,Quarl.Appl.Math,42 (1984),113-117.
[9]	Z.-H.Xiong and Q.-S.Zheng,General algorithms for the polar decomposition and strains,Acta Mech.Sinica,4(1988),175-181.
[10]	Q.-S.Zheng,Theory of representations for tensor functions——A unified invariant approach to constitutive equations,Appl.Mech.Rer.,47 (1994),545-587.中译:张量函数为表示理论—术构方程统一不变性研究,力学进展,26(1) (1996),114-137和26(2) (1996).