A new approach is proposed for nonlinear boundary element methods in computing internal stresses accurately using a complex-variable formulation. In this approach, the internal stresses are obtained from the numerical derivatives of the displacement integral equations that involve only weakly singular integrals. The collocation points in the displacement integral equations are dened as complex variables whose imaginary part is a small step size for numerical derivatives. Unlike the finite difference method whose solution accuracy is step-size dependent, the complex-variable technique can provide ‘‘numerically-exact’’ derivatives of complicated functions, which is step-size independent in the small asymptotic limit. Mean while, it also circumvents the tedious analytical differentiation in the process. Consequently, the evaluation of the nonlinear stress increment only deals with kernels no more singular than that of the displacement increment. In addition, this technique can yield more accurate stresses for nodes that are near the boundary. Three examples are presented to demonstrate the robustness of this method.

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.

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, 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.

This paper presents a new inverse analysis approach for identifying material properties and unknown geometries for multi-region problems using the Boundary Element Method (BEM). In this approach, the material properties and coordinates of an unknown region boundary are taken as the optimization variables, and the sensitivity coefficients are computed by the Complex-Variable-Differentiation Method (CVDM). Due to the use of CVDM, the sensitivity coefficients can be accurately determined in a way that is as simple to use as the Finite Difference Method (FDM) and an inverse analysis for a complex composite structure can be easily performed through a similar procedure to the direct computation. Although basic integral equations are presented for heat conduction problems, the application of the proposed algorithm to other problems, such as elastic problems, is straightforward. Two numerical examples are given to demonstrate the potential of the proposed approach.