Solving Elastic Problems with Local Boundary Integral Equations (LBIE) and Radial Basis Functions (RBF) Cells

CMES: Computer Modeling in Engineering & Sciences, 57(2) (2010), 109-135
http://dx.doi.org/10.3970/cmes.2010.057.109

A new Local Boundary Integral Equation (LBIE) method is proposed for the solution of plane elastostatic problems. Non-uniformly distributed points taken from a Finite Element Method (FEM) mesh cover the analyzed domain and form background cells with more than four points each. The FEM mesh determines the position of the points without imposing any connectivity requirement. The key-point of the proposed methodology is that the support domain of each point is divided into parts according to the background cells. An efficient Radial Basis Functions (RBF) interpolation scheme is exploited for the representation of displacements in each cell. Tractions in the interior domain are avoided with the aid of the companion solution. At the intersections between the local domains and the global boundary, tractions are treated as independent variables with the use of conventional boundary elements. Criteria about the size of the support domains are provided. The integration in support domains is performed easily, fast and with high accuracy. Due to the geometric information provided by the cells the extension of the method to three dimensions is straightforward. Three representative numerical examples demonstrate the achieved accuracy of the proposed LBIE methodology.