具有抛物线边界的各向异性体的二维变形问题

Two-Dimensional Deformation of an Anisotropic Elastic Body with a Parabolic Boundary

Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai

摘要: 文章通过Lekhnitskii方法及映射函数法系统地研究了具有抛物线边界的各向异性体的二维变形问题,并利用所获得的结果研究了一种特殊的结构--半无限裂纹问题,求得了裂纹尖端的应力奇异场及应力强度因子。
- Lekhnitskii方法 /
- 特征值 /
- 应力强度因子
Abstract: In.the present paper,two-dimenstional deformation problems of an anisotropic boby.with a parabolic boundary.are sysiematically analysed by using Lekhnitskii's formalism and the mapping functions method.then a special.structure-the half-infinite crack problem is studied through the obtained results.the sinular fields and the sress iniensity factors near the crack tip are also obiained.
- Lekhnitskii method /
- eigenvalue /
- stress intensity factor

[1]	钱伟长、叶开沅,《弹性力学》,科学出版社(1980).
[2]	徐芝纶,《弹性力学》,科学出版社(1985).
[3]	Eshelby,J.D.,W.T.Read and W.Shoekley,Anisotropie elasticity with applications to dislocation theory,Acta Metal,1(1953),251-259.
[4]	Stroh,A.N.,Dislocations and cracks in anisotropie elasticity.Phys.Mag.3(1985).625-646.
[5]	Stroh,A.N.,Steady-state problems in anisotropic elasticity,J.Math.Phys,41(1962).77-103.
[6]	Barnett,D.M.and J.Lothe,An image force theorem for dislocations in anisotropir bicrystals,J.Phys.F.,4(1974),1618-1635.
[7]	Barnett.D.M.,and J.Lothe,K.Nishioka and R.J.Asaro,Elastic surface wines in anisotropic crystals:a simplified method for calculating Rayleigh velocities using dislocation theory,J.Phys.F.,3(1973),1083-1096.
[8]	Lothe,J.and D.M.Barnett,On the existence of surface-wave solutions for anisotropic elastic half-spaces with free surface.J.Appl.Phys.,47(1976).428-433.
[9]	Asaro,R.J.,and J.P.Hirth,D.M.Barnett and J.Lothe.The elastic energy of a straight dislocation in an infinite anisotropoic elastic medium.Phys.Stat.Sol.B.60(1973),261-271.
[10]	Lekhnitskii,S.G.,Theory of Elasticity of Anisotropic Body,MIR,Moscow(1981).
[11]	Wang,S,S,and I.Choi.Boundary layer thermal stress in angle-ply composite laminates Modern Developments in Composite Materials and Structures,ASME,Edited by 7.R.Virstor(1979),315-341.
[12]	Sih,G.C,and H.Liebowitz,Mathematical theory of Brittle fracture,in An Advanced Treatise on Fracture,Ed,H,Liebowitz,Academic Ptess(1988).67-190.