This paper describes a robust and efficient elasto-plastic boundary element method (BEM) intended for complex problems in geomechanics. Some novel techniques are employed to evaluate the singular integral equations accurately and efficiently. In particular, the strong singularities arising in the domain integrals of the stress integral equations are removed by transforming them from domain integrals to (cell) boundary integrals. Adaptive integration schemes are used throughout to optimize the integration process. The system equations are condensed by recasting them in terms of the plastic multiplier, and a novel Newton–Raphson algorithm delivers greatly improved solution times. Some examples demonstrate the scope and power of the method.

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.

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.

In this paper, an approach is presented for the numerical evaluation of weakly, strongly, hyper- and super-singular boundary integrals which exist in the Cauchy principal value sense in two-dimensional problems. In this approach, the singularities involved in integration kernels are analytically removed by expressing the nonsingular parts of the integration kernels as polynomials of the distance r. A self-contained Fortran code is listed and described for implementation of the proposed approach. The attached code is also able to evaluate general regular integrals using Gaussian quadrature, which enables the code to evaluate any two-dimensional boundary integral. Some examples are provided to verify the correctness of the presented formulations and the included code.

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.