Yan Gu

Analysis of three-dimensional anisotropic heat conduction problems on thin domains using an advanced boundary element method

Abstract In this paper, an advanced boundary element method (BEM) is developed for solving three-dimensional (3D) anisotropic heat conduction problems in thin-walled structures. The troublesome nearly singular integrals, which are crucial in the applications of the BEM to thin structures, are calculated efficiently by using a nonlinear coordinate transformation method. For the test problems studied, promising BEM results with only a small number of boundary elements have been obtained when the thickness of the structure is in the orders of micro-scales (10 −6 ), which is sufficient for modeling most thin-walled structures as used in, for example, smart materials and thin layered coating systems. The advantages, disadvantages as well as potential applications of the proposed method, as compared with the finite element method (FEM), are also discussed.

Three-dimensional thermal stress analysis using the indirect BEM in conjunction with the radial integration method

Abstract Thermal stress analysis is one of key aspects in mechanical design. Based on the indirect boundary integral equation (BIE) and the radial integration method (RIM), this paper develops a boundary-only element method for the boundary stress analysis of three-dimensional (3D) static thermoelastic problems. A transformation system constructed with the normal and two special tangential vectors is used to regularize the singularity in the indirect BIE. The RIM is then employed to transform the domain integrals arising in both displacement and its derivative integral equations into the equivalent boundary integrals, which results in a pure boundary discretized algorithm. Several numerical experiments are provided to verify the accuracy and convergence of the present approach.

Fast multipole singular boundary method for Stokes flow problems

Abstract This paper firstly employs the fast multipole method (FMM) to accelerate the singular boundary method (SBM) solution of the Stokes equation. We present a fast multipole singular boundary method (FMSBM) based on the combination of the SBM and the FMM. The proposed FMSBM scheme reduces CPU operations and memory requirements by one order of magnitude, namely O ( N ) (where N is the number of boundary nodes). Thus, the strategy overcomes costly expenses of the SBM due to its dense interpolation matrix while keeping its major merits being free of mesh, boundary-only discretization, and high accuracy in the solution of the Stokes equation. The performance of this scheme is tested to a few benchmark problems. Numerical results demonstrate its efficiency, accuracy and applicability.

A meshless average source boundary node method for steady-state heat conduction in general anisotropic media

Abstract The average source boundary node method (ASBNM) is a recent boundary-type meshless method, which uses only the boundary nodes in the solution procedure without involving any element or integration notion, that is truly meshless and easy to implement. This paper documents the first attempt to extend the ASBNM for solving the steady-state heat conduction problems in general anisotropic media. Noteworthily, for boundary-type meshless/meshfree methods which depend on the boundary integral equations, whatever their forms are, a key but difficult issue is to accurately and efficiently determine the diagonal coefficients of influence matrices. In this study, we develop a new scheme to evaluate the diagonal coefficients via the pure boundary node implementation based on coupling a new regularized boundary integral equation with direct unknowns of considered problems and the average source technique (AST). Seven two- and three-dimensional benchmark examples are tested in comparison with some existing methods. Numerical results demonstrate that the present ASBNM is superior in the light of overall accuracy, efficiency, stability and convergence rates, especially for the solution of the boundary quantities.