摘要:
在连续介质力学中不仅Cauchy六方程 是不完善的,而且著名的Cauchy运动定律(式中,,ρb,T及divT是连续的)也是不完善的[2].前六个方程的不完善是由于在空间给定点上变形的几何表示方法至今尚非完全[3],而后两个定律的不完善则Cauchy自己解释说ρb,T及divT是标架无关的,但则不是,且T是对称的[2].因此我们说后两个定律不可能满足广义标架上的非对称张量.本文的目的是在三维牵引力域的影响下用广义标架上的非对称张量来完善Cauchy运动定律.
Abstract:
In continuum mechanics.Cauchy's six equations are incomplete[1] and the famous Cauchy's laws of motion where ,ρb,T and divT are continuous are also incomplete[2].The first six equations are incomplete because the geometrical representation of deformation at a given point is as yet incomplete[3],and the last two laws are incomplete because b,T and divT are frame-indifferent,but is not,and T is a symmetric,as Cauchy interpreted himself.Therefore,we say,the last two laws can't accommodate to the asymmetric tensor.The purpose of this paper is to complete Cauchy's laws of motion by postulating an asymmetric tensor for the underlying traction field of 3-dimensional space on a general framing.
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