Extended wavelet Galerkin method for mixed-mode cracked FGM plate under static and dynamic loads

Abstract

The extended wavelet Galerkin method (XWGM) is presented for fracture mechanics analysis of functionally graded material (FGM) cracked plates under static and dynamic loads. The nonhomogeneous stress distribution and stress wave transition can be approximated by the piecewise truncated polynomial (B-spline) functions. The steep stress gradients around the crack tip can be captured by superposing the higher resolution wavelet functions with the nature of multiresolution analysis (MRA) in the wavelet theory. Additionally, a trigonometric function and Heaviside function are employed to enrich the wavelet bases for the fracture modeling. The interaction integral method is utilized to evaluate the static and dynamic mixed-mode stress intensity factors taking the inertia and material nonhomogeneity into account. Applicability of XWGM to the FGM crack problems is discussed through the numerical examples.