Applied Mathematics and Mechanics (English Edition) ›› 1992, Vol. 13 ›› Issue (11): 1067-1076.

• 论文 • 上一篇    

THE TRACTION PROBLEM IN ELASTODYNAMICS

谷安海   

  1. China Great Wall Aluminum Corporation, Zhengzhou
  • 收稿日期:1990-03-06 出版日期:1992-11-18 发布日期:1992-11-18

THE TRACTION PROBLEM IN ELASTODYNAMICS

Gu An-hai   

  1. China Great Wall Aluminum Corporation, Zhengzhou
  • Received:1990-03-06 Online:1992-11-18 Published:1992-11-18

摘要: In continuum mechanics. Cauchy’s six equations

are incomplete[1] and the famous Cauchy’s laws of motion

where ρx, 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 ρx 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.

关键词: traction, weightlessness, asymmetric, tensor

Abstract: In continuum mechanics. Cauchy’s six equations

are incomplete[1] and the famous Cauchy’s laws of motion

where ρx, 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 ρx 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.

Key words: traction, weightlessness, asymmetric, tensor

APS Journals | CSTAM Journals | AMS Journals | EMS Journals | ASME Journals