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 and simple boundary-domain integral equation is presented for heat conduction problems with heat generation and non-homogeneous thermal conductivity. Since a normalized temperature is introduced to formulate the integral equation, temperature gradients are not involved in the domain integrals. The Green’s function for the Laplace equation is used and, therefore, the derived integral equation has a unified form for different heat generations and thermal conductivities. The arising domain integrals are converted into equivalent boundary integrals using the radial integration method (RIM) by expressing the normalized temperature using a series of basis functions and polynomials in global co-ordinates. Numerical examples are given to demonstrate the robustness of the presented 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.

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, explicit boundary-domain integral equations for evaluating velocity gradients are derived from the basic velocity integral equations. A free term is produced in the new strongly singular integral equation, which is not included in recent formulations using the complex variable differentiation method (CVDM) to compute velocity gradients (Int. J. Numer Meth. Fluids 2004; 45:463-484; Int. J. Numer Meth. Fluids 2005; 47:19-43). The strongly singular domain integrals involved in the new integral equations are accurately evaluated using the radial integration method (RIM). Considerable computational time for evaluating integrals of velocity gradients can be saved by using present formulation than using CVDM. The formulation derived in this paper together with those presented in reference (Int. J. Numer. Meth. Fluids 2004; 45:463-484) for 2D and in (Int. J. Numer Meth. Fluids 2005; 47:19-43) for 3D problems constitutes a complete boundary-domain integral equation system for solving full Navier-Stokes equations using primitive variables. Three numerical examples for steady incompressible viscous flow are given to validate the derived formulations. Copyright 2007 John Wiley & Sons, Ltd.