In this paper, an isotropic elastic damage analysis is presented by using a meshless boundary element method (BEM) without internal cells. First, nonlinear boundary-domain integral equations are derived by using the fundamental solutions for undamaged, homogeneous, isotropic and linear elastic solids and the concept of normalized displacements, which results in boundary-domain integral equations without an involvement of the displacement gradients in the domain-integral. Then, the arising domain-integral due to the damage effects is converted into a boundary integral by approximating the normalized displacements in the domain-integral by a series of prescribed radial basis functions (RBF) and using the radial integration method (RIM). The damage variable used in the paper is the ratio of the damaged area to the total area of the material, and an exponential evolution equation for the damage variable is adopted. A numerical example is given to demonstrate the efficiency of the present meshless BEM.

In this paper, a new boundary element method for the interaction between frictional bolts and rock mass is presented by formulating the surface frictional forces of the bolts in terms of the displacements of the rock mass. The corresponding formulation for the underground openings supported by frictional bolts is derived. The action of the bolts on the rock mass is reduced to line integrals along the bolt length. Then the bolts are discretized into a number of quadratic elements. Analytical expressions are obtained when the source point coincides with one of the element nodes. Formulations for calculating the stress at internal points are also presented. The algebraic equations are established by the usual nodal collocation scheme. A computer code for the approach has been written based on the linear element program. Finally, two examples are presented to demonstrate the effectiveness of this method.

A nonlinear elastic boundary element method (NBEM) approach is developed as an innovative deforming mesh generator for computational aeroelastic simulation. The computational fluid dynamics (CFD) mesh is assumed to be embedded in an in finite nonlinear elastic medium of a hardening material, leading to the formulation of apseudononlinear elastostatic problem. Whereas the CFD surface mesh is treated as a boundary element model and the CFD flow field grid as domain sample points, the NBEM approach solves Navier’s equations using a particular solution scheme that removes the requirement of the domain integral in the conventional NBEM formulation. The NBEM approach has a unified feature that is applicable to all mesh systems, including unstructured, multiblock structured, and overset grids. An optimization strategy is employed to determine the optimum hardening material properties by minimizing the mesh distortion in the viscous region where grid orthogonality must be preserved. Three test cases are performed to demonstrate the robustness and effectiveness of the NBEM approach for deforming mesh generation.

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. q 2002 Elsevier Science Ltd. All rights reserved.

Novel methods are described for removing the strong singularities arising in the domain integrals of elastoplasticity, and for solving the non-linear equation set. The former employs a new transformation from domain integrals to (cell) boundary integrals. The number of system equations is minimised by using the plastic multiplier as the primary unknown and an incremental variable stiffness iterative algorithm is developed for solving these equations. Excellent convergence is achieved and some numerical examples demonstrate the algorithm's effectiveness.