SGBEM (Using Non-hyper-singular Traction BIE), and Super Elements, for Non-Collinear Fatigue-growth Analyses of Cracks in Stiffened Panels with Composite-Patch Repairs

Two-dimensional weakly-singular Symmetric Galerkin Boundary Elements (SGBEMs) are developed, following the work of [Han and Atluri (2003)], using non-hypersingular integral equations for tractions. Specifically, the present 2D SGBEM is used to compute the stress intensity factors for arbitrary-shaped line cracks, including embedded, edge, branching, and intersecting cracks. The computed stress intensity factors show high accuracy, even with very coarse meshes. The non-collinear mixed-mode fatigue growth analysis of cracks requires a very minimal effort—simply extending the cracks by adding an element to each crack tip, in the direction of the crack-growth as determined by a physics-based criterion. Moreover, by rearranging the symmetric Galerkin boundary integral equations, a Super Element containing the arbitrarily growing crack is developed. The Super Element is an arbitrarily-shaped domain with or without cracks inside it. Each Super Element has a stiffness matrix and a force vector, which have physical meanings similar to those by traditional finite elements.Likewise, the stiffness matrix of the Super Element is also positive semi-definite and has exactly three rigid body modes. Super Elements can therefore be directly coupled with traditional finite elements, using the simple assembly procedure. Super Elements are thus very suitable for analyzing large-scale structures and complex structures with cracks growing under fatigue. Fatigue analysis of cracked thin panels with stiffeners and composite patches are presented, showing the simplicity and efficiency of using SGBEM Super Elements to model cracked and repaired stiffened aircraft structures.