A quadtree-polygon-based scaled boundary finite element method for crack propagation modeling in functionally graded materials
- Authors: Chen, Xiaojun , Luo, Tao , Ooi, Ean Tat , Ooi, Ean Hin , Song, Chongmin
- Date: 2018
- Type: Text , Journal article
- Relation: Theoretical and Applied Fracture Mechanics Vol. 94, no. (2018), p. 120-133
- Full Text: false
- Reviewed:
- Description: This paper presents a method to improve the computational efficiency of the scaled boundary finite element formulation for functionally graded materials. Both isotropic and orthotropic functionally graded materials are considered. This is achieved using a combination of quadtree and polygon meshes. This hybrid meshing approach is particularly suitable to be used with the SBFEM for functionally graded materials because of the significant amount of calculations required to compute the stiffness matrices of the polygons/cells in the mesh. When a quadtree structure is adopted, most of the variables required for the numerical simulation can be pre-computed and stored in the memory, retrieved and scaled as required during the computations, leading to an efficient method for crack propagation modeling. The scaled boundary finite element formulation enables accurate computation of the stress intensity factors directly from the stress solutions without any special post-processing techniques or local mesh refinement in the vicinity of the crack tip. Numerical benchmarks demonstrate the efficiency of the proposed method as opposed to using a purely polygon-mesh based approach. © 2018 Elsevier Ltd
Numerical investigation of the meshless radial basis integral equation method for solving 2D anisotropic potential problems
- Authors: Ooi, Ean Hin , Ooi, Ean Tat , Ang, Whye Teong
- Date: 2015
- Type: Text , Journal article
- Relation: Engineering Analysis with Boundary Elements Vol. 53, no. (2015), p. 27-39
- Full Text: false
- Reviewed:
- Description: The radial basis integral equation (RBIE) method is derived for the first time to solve potential problems involving material anisotropy. The coefficients of the anisotropic conductivity require the gradient term to be modified accordingly when deriving the boundary integral equation so that the flux expression can be properly accounted. Analyses of the behavior of the anisotropic fundamental solution and its spatial gradients showed that their variations along the subdomain boundaries may be large and they increase as the diagonal components of the material anisotropy become larger. The accuracy of the anisotropic RBIE was found to depend primarily on the accuracy of the influence coefficients evaluations and this precedes the number of nodes used. Root mean squared errors of less than 10(-4)% can be obtained if evaluations of the influence coefficients are sufficiently accurate. An alternative formulation of the anisotropic RBIE was derived. The levels of accuracy obtained were not significantly different from the standard formulation. (C) 2014 Elsevier Ltd. All rights reserved.