Three-Dimensional Fracture Analysis in Functionally Graded Materials Using the Finite Block Method in Strong Form

In this paper, the application of the strong-form finite block method (FBM) to three-dimensional fracture analysis with functionally graded materials is presented. The main idea of the strong-form FBM is that it transforms the arbitrary physical domain into a normalized domain and utilizes the direct collocation method to form a linear system. Using the mapping technique, partial differential matrices of any order can be constructed directly. Frameworks of the strong-form FBM for three-dimensional problems based on Lagrange polynomial interpolation and Chebyshev polynomial interpolation were developed. As the dominant parameters in linear elastic fracture mechanics, the stress intensity factors with functionally graded materials (FGMs) were determined according to the crack opening displacement criteria. Several numerical examples are presented using a few blocks to demonstrate the accuracy and efficiency of the strong-form FBM.