Meshless variational method applied to Mixed-mode dynamic stress intensity factors

Abstract

For linear elastic fracture mechanics, the variational technique with a path independent contour integral is used to determine the stress intensity factors (SIFs) for functionally graded materials (FGMs) under static and dynamic loads in this work. Utilizing the interpolation of the Chebyshev polynomials and the finite block method (FBM) to deal with two-dimensional fracture problems. The Quadratic form block is transformed from Cartesian coordinates to normalized coordinates with 8 nodes by technology of mapping. The new equilibrium equations in terms of displacements are derived in a normalized coordinate system. All coefficients of the Chebyshev polynomials are determined by considering the governing equations, boundary conditions and connecting conditions of the two blocks. The accuracy and convergence of the FBM with Chebyshev polynomials are illustrated through several examples and comparison has been implemented with analytical solutions and different numerical approaches.