SGBEM (for Cracked Local Subdomain) -- FEM (for uncracked global Structure) Alternating Method for Analyzing 3D Surface Cracks and Their Fatigue-Growth

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 improvement is formulated and implemented for the analyses of three-dimensional arbitrary surface cracks by modeling the cracks in a local finite-sized subdomain using 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 solution for the cracked structural component is obtained in an iteration procedure, which alternates between FEM solution for the uncracked body, and the SGBEM solution for the crack in the local finite-sized subdomain. The regularized version of the displacement and traction 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 direction of tensile loading in a plate, is studied; and the mixed-mode fatigue-crack-growth results are compared with experimental data reported in literature. keyword: SGBEM, FEM, alternating, surface crack.

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