A novel approach to crack modeling using extended finite element and substructures methods

Abstract

In the present work, a combination of Extended Finite Element Method (XFEM) and substructures methods has been utilized for crack modeling. Structures are divided into several substructures, and XFEM is employed to model the presence of cracks within each substructure. In another method, crack modeling has been carried out without using the Extended Finite Element Method. Instead, cracks are modeled by eliminating boundary constraints from two substructures. The Krylov-Schur algorithm is utilized to accelerate the computation of structural modes by preparing stiffness and mass matrices for eigenvalue and eigenvector calculations related to the superstructure. For evaluating this method, four examples have been considered: In the first example, an experimental L-shaped steel structure comprising a beam and a column was examined. The second example involved an experimental steel beam with a box-shaped cross-section. In the third example, a steel beam with simple supports at both ends and a rectangular cross-section was proposed. In the fourth example, a real two-span bridge (Turtle Mountain Bridge) is also presented to evaluate the proposed method. The method was applied for modeling, and the obtained results were validated using experimental and analytical results. In this work, the Structural Similarity Index Method (SSIM) for mode shape similarity assessment has been employed for crack identification. Based on the results obtained from the modeling and crack identification evaluations, it can be concluded that the current method can model multiple cracks in structures with variable cross-sections, real concrete bridges, frame-shaped structures, and diverse structures by assembling substructures. Despite simplifying the problems, it maintains an acceptable level of accuracy in validation. This advantage enables the identification of cracks through a straightforward comparison of mode shapes.