Modified equilibrium on line method for imposition of Neumann boundary conditions in meshless collocation methods

A modified version of the equilibrium on line method (ELM) for imposition of Neumann boundary conditions in collocation methods is presented. In the ELM, equilibrium on lines in the local coordinate systems on the Neumann boundary is satisfied as Neumann boundary condition equations. In other words, integration domains are straight lines for nodes located on the Neumann boundary. Furthermore, the Heaviside function is used as a weight in these integrals. In this paper, a modified procedure for choosing the integration domains is proposed. Also, application of different test functions is examined. The performance of the modified version of the ELM is studied for collocation methods based on two different methods to construct meshless shape functions: moving least-squares approximation and radial basis point interpolation. Also, the effects of these two meshless interpolation parameters are investigated. Numerical examples of two-dimensional linear and generalized nonlinear Poisson's equation, linear elasticity and elasto-plastic analysis are presented to demonstrate the stability, accuracy and convergence of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.