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非均匀切向荷载下弹性半空间二阶效应的一般解答*

刘又文 郭建林

刘又文, 郭建林. 非均匀切向荷载下弹性半空间二阶效应的一般解答*[J]. 应用数学和力学, 1997, 18(4): 341-355.
引用本文: 刘又文, 郭建林. 非均匀切向荷载下弹性半空间二阶效应的一般解答*[J]. 应用数学和力学, 1997, 18(4): 341-355.
Liu Youwen, Gou Jianlin. The General Solution of Second order Effects in Elastic Half-Space Acted upon by a Non-Uniform Shear Load[J]. Applied Mathematics and Mechanics, 1997, 18(4): 341-355.
Citation: Liu Youwen, Gou Jianlin. The General Solution of Second order Effects in Elastic Half-Space Acted upon by a Non-Uniform Shear Load[J]. Applied Mathematics and Mechanics, 1997, 18(4): 341-355.

非均匀切向荷载下弹性半空间二阶效应的一般解答*

基金项目: * 湖南省自然科学基金

The General Solution of Second order Effects in Elastic Half-Space Acted upon by a Non-Uniform Shear Load

  • 摘要: 继文[1],本文运用积分变换方法,获得了可压缩各向同性弹性半空间在非均匀分布的切向荷载下,二阶弹性效应问题的封闭形式一般解答.
  • [1] 刘又文、郭建林,非r均匀法向载荷下半空问的二阶弹性效应问题,应用数学和力学,15(12)(1994).1091-1110.
    [2] R.S.Rivlin,The solution of problems in second order elasticity theory,J.Ration.Mech.Analysis,2(1953),52.
    [3] A.E.Green and E.B.Spratt,Second order effect in the deformation of elastic solids,Proc.R.Soc.London,A224(1954),347.
    [4] C.A.Truesdell and W.Noll,The Nonlinear Field Theories of Mechanics,Handbuch der Physik(Ed.S.Flugge),Vol.Ⅲ/3,Springer-Verlag,Berlin(1965).
    [5] A.E.Green and J.E.Adkins,Large Elastic Deformations(2nd ed.),Oxford University Press(1970).
    [6] W.H.Goodman and P.M.Naghdi,The use of displacement potentials in second orderelasticity,J.Elasticity,22(1989),25.
    [7] C.Chan and D.E.Carlson,Second order incompressible elastic torsion,Int.J Engrg.Sci.,8(1970),415.
    [8] A.P.S.Selvadurai and A.J.M.Spencer,Second-order elasticity with axial symmetry-I,General theory,Int.J.Engrg.Sci.,10(1972),97.
    [9] M.M.Carroll and F.J.Mooney,Simplification of the second-order problem forincompressible elastic solids,Q.J.Mech.Appl.Math.,37(1984),261.
    [10] K.L.Lindsay,A problem in second order elasticity,J.Elasticity,15(1985),335.[11] I.Choi and R.T.Shield,Second-order effects in problems for a class of elastic materials,Z.Angew.Math.Phys.,32(1981),361.
    [11] A.Signorini,Transformazioni termoelastiche finite,Annali Mat.Pure Appl.,30(1949),10.[13] F.Stoppeli,Un teorema di esistenza e di unicita relativo alle equazioni dell' elastostaticaisoterma per deformazioni finite,Ricerche Mat.,3(1954),247~267.
    [12] F.Stoppeli,Sulla svilluppabilita in serie di potenze di un parametro delle soluzioni delleequazioni dell' elastostatica isoterma,Ric.Mat.,4(1955),58~73.
    [13] I.N.Sneddon,The Use of Transform Methods in Elasticity,Tech.Report.AFOSR64~1789,North Carolina State University,Rayleigh,N.C.(1964).
    [14] V.Cerruti,Rierehe intono all equilibric de corpi elastici isotropi,Atti.Accord.NazL Lincei.Me.Classe,Sci.Fis.Met.Nat.,13(1882),81.
    [15] R.Muki,Asymmetric problems of the theory of elasticity for a send-infinite solid and a thickplate,in Progress in Solid Mechanics,I.N.Sneddon and R.Hill Editors,North-Holland Publish Co.,Amsterdam(1960),401.
    [16] I.N.Sneddon,On Muki's solutions of the equation of linear elasticity,Int.J.Engrg.Set.,30(1992),1237.
    [17] J.Guo,Second order effects in an elastic half-space acted upon by non-uniform loads,Master thesis,Department of Mathematics and Statistics,University of Windsor(1992).
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出版历程
  • 收稿日期:  1995-09-11
  • 修回日期:  1996-09-20
  • 刊出日期:  1997-04-15

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