Abstract
This paper presents crack propagation analyses using the wavelet finite element method. The wavelet finite element method is a new methodology to solve partial differential equations. In the authors' previous studies, solid/structural mechanics analyses without cracks were performed. In the wavelet finite element analysis, the scaling functions are placed throughout the domain of analysis and it is divided by equally spaced structured cells to integrate the stiffness matrices. To improve the accuracy, wavelet functions are superposed on the scaling functions within the regions of high stress concentration, such as the vicinities of hole edge, crack tip, etc.However, since all the basis functions in the wavelet finite element method are assumed to be continuous, there are difficulties in treating displacement jumps across the crack face. In present research, we propose that the discontinuous displacement functions and crack tip asymptotic solution are introduced based on the concept of X-FEM. The proposed method can perform the crack propagation analysis without any remeshings. In this paper, the mathematical formulations of the wavelet finite element method for the crack propagation analysis and its numerical implementations are described. Then, some two dimensional crack propagation analyses are presented for illustrative purposes.
