Kinematically admissible meshless approximation using modified weight function

In meshless methods, in general, the shape functions do not satisfy Kronecker delta properties at nodal points. Therefore, imposing essential boundary conditions is not a trivial task as in FEM. In this regard, there has been a great deal of endeavor to find ways to impose essential boundary conditions. In this study, a new scheme for imposing essential boundary conditions is developed. Weight functions are modified by multiplying with auxiliary weight functions and the resulting shape functions satisfy Kronecker delta properties on the boundary nodes. In addition, the resulting shape functions possess linear interpolation features on the boundary segments where essential boundary conditions are prescribed. Therefore, the essential boundary conditions can be exactly satisfied with the new method. More importantly, the imposition of essential boundary conditions using the present method is infinitely easy as in the finite element method. Numerical examples show that the method also retains high convergence rate comparable to the Lagrange multiplier method. Copyright © 2001 John Wiley & Sons, Ltd.