Traction boundary elements for cracks in anisotropic solids

A general mixed boundary element approach based on displacement and traction integral equations for anisotropic media is presented. Integration of the singular and hypersingular kernels along general quadratic line elements is carried out by analytical transformation of the integrals into regular ones, which are numerically evaluated, plus simple singular integrals with known analytical solution. This is achieved by the simple election of an integration variable, which is consistent with that of the anisotropic fundamental solution. The generality of the method allows for the use of curved elements and discontinuous quarter-point elements to represent Fracture Mechanics problems. Stress Intensity Factors are accurately computed from the crack opening displacement at the nodes of the quarter-point element. Several examples, including curved crack geometries and different material properties are presented. q 2003 Elsevier Ltd. All rights reserved.

[1]  George J. Tsamasphyros,et al.  Gauss quadrature rules for finite part integrals , 1990 .

[2]  Ernian Pan,et al.  Fracture mechanics analysis of cracked 2-D anisotropic media with a new formulation of the boundary element method , 1996 .

[3]  E. Ladopoulos.  On the numerical evaluation of the general type of finite-part singular integrals and integral equations used in fracture mechanics , 1988 .

[4]  Rafael Gallego,et al.  Hypersingular quarter‐point boundary elements for crack problems , 1995 .

[5]  Y. L. Gao,et al.  Boundary element analysis of plane anisotropic bodies with stress concentrations and cracks , 1992 .

[6]  C. Hong,et al.  Application of the Jk integral to mixed mode crack problems for anisotropic composite laminates , 1990 .

[7]  D. Rooke,et al.  The dual boundary element method: Effective implementation for crack problems , 1992 .

[8]  T. Cruse,et al.  Interactive Program for Analysis and Design Problems in Advanced Composites Technology , 1971 .

[9]  M. H. Aliabadi,et al.  Fracture mechanics analysis of anisotropic plates by the boundary element method , 1993 .

[10]  T. Cruse,et al.  Boundary-integral equation analysis of cracked anisotropic plates , 1975 .

[11]  P. Sollero,et al.  Anisotropic analysis of cracks in composite laminates using the dual boundary element method , 1995 .

[12]  E. Dill,et al.  Theory of Elasticity of an Anisotropic Elastic Body , 1964 .

[13]  P. C. Paris,et al.  On cracks in rectilinearly anisotropic bodies , 1965 .

[14]  Morton Lowengrub,et al.  Some Basic Problems of the Mathematical Theory of Elasticity. , 1967 .

[15]  D. P. Rooke,et al.  Anisotropic analysis of cracks emanating from circular holes in composite laminates using the boundary element method , 1994 .

[16]  J. Domínguez,et al.  Three-dimensional fracture analysis in transversely isotropic solids , 1997 .

[17]  C. E. Freese,et al.  Central crack in plane orthotropic rectangular sheet , 1972 .

[18]  T. Cruse,et al.  Stress intensity factors for anisotropic compact-tension specimens with inclined cracks , 1986 .

[19]  K. Gandhi.  Analysis of an inclined crack centrally placed in an orthotropic rectangular plate , 1972 .

[20]  E. Pan,et al.  A general Boundary Element Analysis of 2-D Linear Elastic Fracture Mechanics , 1997 .

[21]  Frank J. Rizzo,et al.  A Method for Stress Determination in Plane Anisotropic Elastic Bodies , 1970 .