unctionally graded materials (FGMs). A meshless boundary element method (BEM) is developed for this purpose. Young’s modulus of the FGMs is assumed to have an exponential variation, while Poisson’s ratio is taken as constant. Since no simple fundamental solutions are available for general FGMs, fundamental solutions for homogeneous, isotropic and linear elastic solids are used in the present BEM, which contains a domain-integral due to the material non-homogeneity. Normalized displacements are introduced to avoid displacement gradients in the domain-integral. The domain-integral is transformed into a boundary integral along the global boundary by using the radial integration method (RIM). To approximate the normalized displacements arising in the domain-integral, basis functions consisting of radial basis functions and polynomials in terms of global coordinates are applied. Numerical results are presented and discussed to show the accuracy and the efficiency of the present meshless BEM.

In this paper, a new set of boundary-domain integral equations is derived from the continuity and momentum equations for three-dimensional viscous flows. The primary variables involved in these integral equations are velocity, traction, and pressure. The final system of equations entering the iteration procedure only involves velocities and tractions as unknowns. In the use of the continuity equation, a complex-variable technique is used to compute the divergence of velocity for internal points, while the traction-recovery method is adopted for boundary points. Although the derived equations are valid for steady, unsteady, compressible, and incompressible problems, the numerical implementation is only focused on steady incompressible flows. Two commonly cited numerical examples and one practical pipe flow problem are presented to validate the derived equations.

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, 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 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