Characterization and analysis of delamination fracture in composites: An overview of developments from 1990 to 2001

In this paper, a simple and robust method, called the radial integration method, is presented for transforming domain integrals into equivalent boundary integrals. Any two- or three-dimensional domain integral can be evaluated in a unified way without the need to discretize the domain into internal cells. Domain integrals consisting of known functions can be directly and accurately transformed to the boundary, while for domain integrals including unknown variables, the transformation is accomplished by approximating these variables using radial basis functions. In the proposed method, weak singularities involved in the domain integrals are also explicitly transformed to the boundary integrals, so no singularities exist at internal points. Some analytical and numerical examples are presented to verify the validity of this method.

The radial integration method for evaluation of domain integrals with boundary-only discretization

The Hypercircle in Mathematical Physics.

Radial basis functions (RBFs) are constructed in terms of one-dimensional distance variable and appear to have certain advantages over the traditional coordinates-based functions. In contrast to the traditional meshed-based methods, the RBF collocation methods are mathematically simple and truly meshless, which avoid troublesome mesh generation for high-dimensional problems involving irregular or moving boundary. This opening chapter begins with the introduction to RBF history and its applications in numerical solution of partial differential equations and then gives a general overview of the book.

Recent Advances in Radial Basis Function Collocation Methods

A review of T-stress and its effects in fracture mechanics

A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of steady-state and transient heat conduction problems in a continuously non- homogeneous anisotropic medium. The Laplace transform is used to treat the time dependence of the variables for transient problems. The an- alyzed domain is covered by small subdomains with a simple geometry. A weak formulation for the set of governing equations is transformed into local integral equations on local subdomains by using a unit test function. Nodal points are ran- domly distributed in the 3D analyzed domain and each node is surrounded by a spherical subdo- main to which a local integral equation is applied. The meshless approximation based on the Mov- ing Least-Squares (MLS) method is employed for the implementation. Several example problems with Dirichlet, mixed, and/or convection bound- ary conditions, are presented to demonstrate the veracity and effectiveness of the numerical ap-

Analysis of Transient Heat Conduction in 3D Anisotropic Functionally Graded Solids, by the MLPG Method

Treatment of bimaterial interface crack problems using the boundary element method

In this paper, the method of characteristics which has been employed to reduce two-dimensional steady-state anisotropic field problems to ones governed by the simple Laplace equation in a mapped domain, is extended to numerically treat similar three-dimensional problems by the boundary element method (BEM). The proposed process does not involve any rotation of coordinate axes as is normally done in the literature. The advantage of this approach is that the three-dimensional anisotropic field problem can then be easily solved with any readily available BEM programs for three-dimensional ‘isotropic’ potential theory. The validity of the proposed scheme is demonstrated by three numerical examples where the results are compared with those obtained using the finite element method with the commercial code ANSYS.

Choon-Lai Tan

Papers

Analysis of Transient Heat Conduction in 3D Anisotropic Functionally Graded Solids, by the MLPG Method

Treatment of bimaterial interface crack problems using the boundary element method

BEM treatment of three-dimensional anisotropic field problems by direct domain mapping

Fracture mechanics analysis of size-dependent piezoelectric solids

Two-dimensional boundary element contact mechanics analysis of angled crack problems