An adaptive finite element/meshless coupled method based on local maximum entropy shape functions for linear and nonlinear problems

Ullah, Z., Coombs, W.M. and Augarde, C.E. (2013) An adaptive finite element/meshless coupled method based on local maximum entropy shape functions for linear and nonlinear problems. Computer Methods in Applied Mechanics and Engineering, 267, 111 - 132. (doi: 10.1016/j.cma.2013.07.018)

Abstract

Abstract In this paper, an automatic adaptive coupling procedure is proposed for the finite element method (FEM) and the element-free Galerkin method (EFGM) for linear elasticity and for problems with both material and geometrical nonlinearities. In this new procedure, initially the whole of the problem domain is modelled using the FEM. During an analysis, those finite elements which violate a predefined error measure are automatically converted to an {EFG} zone. This {EFG} zone can be further refined by adding nodes, thus avoiding computationally expensive {FE} remeshing. Local maximum entropy shape functions are used in the {EFG} zone of the problem domain for two reasons: their weak Kronecker delta property at the boundaries allows straightforward imposition of essential boundary conditions and also provides a natural way to couple the {EFG} and {FE} regions compared to the use of moving least squares basis functions. The Zienkiewicz and Zhu error estimation procedure with the superconvergent patch method for strains and stresses recovery is used in the {FE} region of the problem domain, while the Chung and Belytschko error estimation procedure is used in the {EFG} region.

• Item Type: Articles
• Keywords: Superconvergent patch recovery
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Ullah, Dr Zahur
• Authors: Ullah, Z., Coombs, W.M., and Augarde, C.E.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: Computer Methods in Applied Mechanics and Engineering
• Publisher: Elsevier
• ISSN: 0045-7825