Dynamic analysis of multi-crack problems by the spline fictitious boundary element method based on Erdogan fundamental solutions

Abstract

The appearance of multiple cracks on engineering structures has a large influence on the structural dynamic characteristics. The Erdogan fundamental solutions for static analysis of an infinite single cracked plate are introduced in this paper. Using the multi-domain coupling technique, the multi-crack problem is transformed into several single crack problems. For each single crack problem, based on the above fundamental solutions, dynamic fracture analysis is presented with the mathematical formulation and computational implementation of the spline fictitious boundary element method (SFBEM). Here, the stress boundary conditions on the crack surface are automatically satisfied and the singular behaviour at the crack tip is naturally captured. The angular frequencies and mode shapes of the multi-crack problem are obtained using the proposed method. The dynamic stress intensity factors (DSIFs) of the multi-crack problem are also obtained. Numerical examples are given to demonstrate the accuracy of the proposed method in comparison to the finite element method.