In this paper, the reciprocal work theorem for viscous fluid flow is established for Newtonian fluids and, based on this theorem, a set of boundary-domain integral equations is derived from the continuity and momentum equations for two-dimensional viscous flow The complex-variable technique is used to compute velocity gradients in the use of the continuity equation. The primary variables involved in these integral equations are velocity, traction and pressure. Although the numerical implementation is only focused on steady incompressible flow, these equations are applicable to solving steady, unsteady, compressible and incompressible problems. In this method, the pressure can be expressed in terms of velocity and traction such that the final system of equations entering the iteration procedure only involves velocity and traction as unknowns. Two commonly cited numerical examples are presented to validate the derived equations.

In this paper, a new and simple boundary element method without internal cells is presented for the analysis of elastoplastic problems, based on an effective transformation technique from domain integrals to boundary integrals. The strong singularities appearing in internal stress integral equations are removed by transforming the domain integrals to the boundary. Other weakly singular domain integrals are transformed to the boundary by approximating the initial stresses with radial basis functions combined with polynomials in global coordinates. Three numerical examples are presented to demonstrate the validity and effectiveness of the proposed method.

A novel set of auxiliary equations, which supplement the fundamental boundary integral equations, for the treatment of corners and edges arising in discontinuous traction problems and at zonal intersections is derived. Based on these equations, an efficient linear 3D multi-region BEM algorithm is presented which can deal with arbitrarily many regions. Numerical examples demonstrate the effectiveness of this algorithm.

this paper presents a new infinite element approach for three-dimensional boundary: element analysis of half-space problems. The strongly singular integrals over the infinite surface are evaluated analytically by transforming the surface integrals into line integrals. The illustrative numerical results demonstrate the potential of the formulation. 0 1998 Elsevier Science Ltd. All rights reserved

In this paper, a set of boundary integrals are derived based on a radial integration technique to accurately evaluate two dimensional (2D) and three dimensional (3D), regular and singular domain integrals. A self-contained Fortran code is listed and described for numerical implementation of these boundary integrals. The main feature of the theory is that only the boundary of the integration domain needs to be discretized into elements. This feature can not only save considerable efforts in discretizing the integration domain into internal cells (as in the conventional method), but also make computational results for singular domain integrals more accurate since the integrals have been regularized. Some examples are provided to verify the correctness of the presented formulations and the included code.