具有抛物线边界的二维弹性介质的Green函数
Green’s Functions of Two-Dimensional Anisotropic Body with a Parabolic Boundary
-
摘要: 文章求解了具有抛物线边界的二维弹性介质的两种Green函数,一种是自由边界问题,另一种是刚性边界问题。我们还求得了当抛物线边界退化成半无限裂纹或半无限刚性裂纹时裂纹尖端的奇异场,得到了集中力作用于边界的基本解,这个基本解使得我们可以通过沿边界积分确定任意分布荷载的弹性解。Abstract: For two-dimensional anisotropic body with a parabolic boundary, the simple explicit expressions of Green's functions are presented when a concentraled force is applied at a point in material for two kind boundary conditions, which are of free surfoce and rigid surface. When parabolic curve degenerales into a half-infinite crack or a half-infinite rigid defect the stress singular fields near the crack tip are obtained by using the results obtained. Specially, when the concentrated force is applied at a point on the parabolic boundary, its Green's functions are studied, too. By them and their integral, the arbitrary parabolic boundary value problems can be solved. The limit case that the boundary degenerates into a crack is studied and the corresponding stress intensity factors are obtained.
-
Key words:
- Stroh’s formalism /
- eigenvalue /
- stress intensity factors
-
[1] T.C.T.Ting,Line forces and dislocations in anisotropic elastic composite wedges and spaces,Phys.Star.Sol.,B146 (1988),81-90. [2] C.Hwu and W.J.Yen,Green's functions of two-dimensional anisotropic plates containing an elliptic hole,Int.J.Sol.Str.,27 (1991),1785-1791. [3] K.Malen,A unified six-dimensional treatment of elastic Green's functions and dislocations,Phys.Status Solidi.,B44 (1971),661-672. [4] T.C.T.Ting,Barnett-Lothe tensors and their associated tensors for monoclinic materials with the symmetric plane at X3=0,J.Elast.,27 (1992),143-165 [5] C.Hwu and T.C.T.Ting,Two-dimensional problems of the anisotropic elastic solid with an elliptic inclusion,QJ.Mech.Appl.Math.,42 (1989),553-572. [6] P.Chadwick and G.D.Smith,Foundations of the theory surface waves in anisotropic elastic medium,Adv.Appl.Mech.,17 (1977),303-376. [7] D.M.Barnett and J.Lothe,Synthesis of the sextic and the integral formalism for dislocations,Green's functions,and surface waves in anisotropic elastic solids.Phys.Norv.,7 (1973),13-19. [8] Z.Suo,Singularities,interfaces and cracks in dissimilar anisotropic media,Proc.R.Soc.Lond.,A427 (1990),331-358. [9] A.N.Stroh,Steady state problem in anisotropic elasticity,J.Math.Phys.,41 (1962),77-103. [10] K.A.Ingebrigtsen and A.Tonning,Elastic surface waves in crystals,Phys,.Rev..184(1969),942-951. [11] A.N.Stroh,Dislocations and cracks in anisotropic elasticity,Phil.Mag.,3 (1958),625-646. [12] J.D.Eshelby,W.T.Read and W.Shockley,Anisotropic elasticity with applications to dislocation theory,Acta Metall.,(1953),251-259. [13] T.C.T.Ting,Image singularities of Green's function for anisotropic elastic half-spaces and bimaterials,J.Elast.,27 (1992),119-139. [14] G.C.Sih and H.Liebowitz,Mathematical theory of brittle fractuer,An Advanced Treatise on Fracture,I,ed.H.Liebowitz,Academic Press (1968),67-190. [15] 胡元太,赵兴华,含椭圆微结构的平面介质的Green函数问题,上海大学学报,1(1) (1995),36-42
点击查看大图
计量
- 文章访问数: 1783
- HTML全文浏览量: 76
- PDF下载量: 677
- 被引次数: 0