A nonlinear elastic boundary element method (NBEM) approach is developed as an innovative deforming mesh generator for computational aeroelastic simulation. The computational fluid dynamics (CFD) mesh is assumed to be embedded in an in finite nonlinear elastic medium of a hardening material, leading to the formulation of apseudononlinear elastostatic problem. Whereas the CFD surface mesh is treated as a boundary element model and the CFD flow field grid as domain sample points, the NBEM approach solves Navier’s equations using a particular solution scheme that removes the requirement of the domain integral in the conventional NBEM formulation. The NBEM approach has a unified feature that is applicable to all mesh systems, including unstructured, multiblock structured, and overset grids. An optimization strategy is employed to determine the optimum hardening material properties by minimizing the mesh distortion in the viscous region where grid orthogonality must be preserved. Three test cases are performed to demonstrate the robustness and effectiveness of the NBEM approach for deforming mesh generation.

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, a set of internal stress integral equations is derived for solving thermoelastic problems.A jump term and a strongly singular domain integral associated with the temperature of the material are produced in these equations. The strongly singular domain integral is then regularizedusing a semi-analytical technique. To avoid the requirement of discretizing the domain into internal cells,domain integrals included in both displacement and internal stress integral equations are transformedinto equivalent boundary integrals using the radial integration method (RIM). Two numerical examples for 2D and 3D, respectively, are presented to verify the derived formulations.