SGBEM (for Cracked Local Subdomain) – FEM (for uncracked global Structure) Alternating Method for Analyzing 3D

Abstract: As shown in an earlier work, the FEM-BEM alternating method is an efficient and accurate method for fracture analysis. In the present paper, a further im-provement is formulated and implemented for the analy-ses of three-dimensional arbitrary surface cracks bymod-eling the cracks in a local finite-sized subdomain us-ing the symmetric Galerkin boundary element method (SGBEM). The finite element method is used to model the uncracked global (built-up) structure for obtaining the stresses in an otherwise uncracked body. The solu-tion for the cracked structural component is obtained in an iteration procedure, which alternates between FEM solution for the uncracked body, and the SGBEM so-lution for the crack in the local finite-sized subdomain. The regularized version of the displacement and trac-tion integral equations and their Galerkin weak forms are used. Examples for surface cracks in a finite-sized global structure demonstrate the accuracy and efficiency of the method. Also, the problem of fatigue-growth of an initially-semi-circular surface flaw, inclined to the di-rection of tensile loading in a plate, is studied; and the mixed-mode fatigue-crack-growth results are compared with experimental data reported in literature