Enrichment of the method of finite spheres using geometry-independent localized scalable bubbles

In this paper, we report the development of two new enrichment techniques for the method of finite spheres, a truly meshfree method developed for the solution of boundary value problems on geometrically complex domains. In the first method, the enrichment functions are multiplied by a weight function with compact support, while in the second one a floating ‘enrichment node’ is introduced. The scalability of the enrichment bubbles offers flexibility in localizing the spatial extent to which the enrichment field is applied. The bubbles are independent of the underlying geometric discretization and therefore provide a means of achieving convergence without excessive refinement. Several numerical examples involving problems with singular stress fields are provided demonstrating the effectiveness of the enrichment schemes and contrasting them to traditional ‘geometry-dependent’ enrichment strategies in which one or more nodes associated with the geometric discretization of the domain are enriched. An additional contribution of this paper is the use of a meshfree numerical integration technique for computing the J -integral using the domain integral method. Copyright 2006 John Wiley & Sons, Ltd.