Gu An-hai. The Traction Problem in Elastodynamics[J]. Applied Mathematics and Mechanics, 1992, 13(11): 1021-1029.
Citation: Gu An-hai. The Traction Problem in Elastodynamics[J]. Applied Mathematics and Mechanics, 1992, 13(11): 1021-1029.

The Traction Problem in Elastodynamics

  • Received Date: 1990-03-06
  • Publish Date: 1992-11-15
  • 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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  • [1]
    Gu An-hai,On the structure of continue and the mathcmatical properties of algeora elastodynamics of a trielinie structural system.Applied Mathematies and Merhanics,8.10(1987),991-1002.
    [2]
    Truesdell.C.,A First Course in Rational Contimum Mechanics.Vol.1.Academic Press.New York,San Francisco.London(1977).50,145-235.
    [3]
    Filonenko-Borodich,M.,Theory of Elastietieiy.Foreign Languages Publishing House,Moskow(30-48).
    [4]
    Crucnbery.K.W.and A.J,Weir.Linear Geometry,Springer-Verlag,NewYork.Heidelberg.Berlin(1977).15-129.
    [5]
    谷安海,线性流型上的变换函数Ф及广义的勾股定理,应用数学和力学,8(12)(1987), 1131-1134.
    [6]
    钱伟长、叶开沅,《弹性力学》,科学出版社(1980),63-64.
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