Premium
Enrichment of the method of finite spheres using geometry‐independent localized scalable bubbles
Author(s) -
Macri Michael,
De Suvranu
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1751
Subject(s) - discretization , meshfree methods , convergence (economics) , scalability , domain (mathematical analysis) , spheres , boundary (topology) , computer science , mathematics , node (physics) , function (biology) , field (mathematics) , numerical analysis , flexibility (engineering) , geometry , finite element method , mathematical optimization , mathematical analysis , pure mathematics , physics , engineering , structural engineering , statistics , database , astronomy , evolutionary biology , economics , biology , economic growth
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.