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.

Semi-Infinite Structure Analysis with Bimodular Materials with Infinite Element.

The modulus of elasticity of some materials changes under tensile and compressive states is simulated by constructing a typical material nonlinearity in a numerical analysis in this paper. The meshless Finite Block Method (FBM) has been developed to deal with 3D semi-infinite structures in the bimodular materials in this paper. The Lagrange polynomial interpolation is utilized to construct the meshless shape function with the mapping technique to transform the irregular finite domain or semi-infinite physical solids into a normalized domain. A shear modulus strategy is developed to present the nonlinear characteristics of bimodular material. In order to verify the efficiency and accuracy of FBM, the numerical results are compared with both analytical and numerical solutions provided by Finite Element Method (FEM) in four examples.