关于时空标架变换和物质标架无关性原理  

ON EUCLIDEAN TRANSFORMATIONS OF SPACE-TIME FRAMES AND PRINCIPLE OF MATERIAL FRAME INDIFFERENCE

作　　者：兰志文[1] 陈良森[1] 扶名福[1] 

机构地区：[1]南昌大学工程力学实验中心,南昌330031

出　　处：《力学学报》2008年第4期502-510,共9页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(10272055)~~

摘　　要：建立了欧几里德标架无关性的一般表述与某一参考标架φ下作相对刚体运动的一般曲线坐标、分量表述之间的关系,从而使欧几里德标架无关性的张量表述有相应的分量表述形式.建立这种联系的基础是,参考标架φ~＊下描述的运动在参考标架φ中某坐标系下的分量结果,对应于φ下另一相对该坐标系作相同刚体运动的坐标系下描述φ观测的运动的分量结果.通过例子说明了Truesdell和Noll用等价动力过程,关于物质标架无关性原理的陈述,比Svendsen和Bertram及Liu的本构关系在参考标架变换下的形式不变性更合理且方便,尤其是对微分方程形式的本构关系更是如此.The main purpose of the present paper is to obtain the relation between the general expression of Euclidean objectivity and the component expression in the general curvilinear coordinate system with a relative rigid motion under a fixed frame φ of reference, so as to the tensor representation of Euclidean objective quantity has its component form. That is, an objective quantity under the reference frame φ＊ has its components with respect to the fixed coordinate system of reference frame φ, while the objective quantity under the reference frame φ has its components relative to another coordinate system of φ with the same relative rigid motion as that of φ and φ＊ to the fixed coordinate system of φ. The two types of components correspond to each other. Moreover, it is exemplified in the present paper that the principle of material frame-indifference with the admissible equivalent dynamic processes of a body by Truesdell and Noll[14] is more convenient than the form-invariance of constitutive equations by Svendsen and Bertram[13] and Liu[4], especially for the rate-form constitutive equations.

关 键 词：欧几里德标架无关性 物质标架无关性 参考标架变换 客观张量 本构关系 

分 类 号：O331[理学—一般力学与力学基础]