Coupling of mesh-free methods with finite elements: Basic concepts and test results

Timon Rabczuk, Shao Ping Xiao, M. Sauer

Research output: Contribution to journalArticle

157 Citations (Scopus)

Abstract

This paper reviews several novel and older methods for coupling mesh-free particle methods, particularly the element-free Galerkin (EFG) method and the smooth particle hydrodynamics (SPH), with finite elements (FEs). We study master-slave couplings where particles are fixed across the FE boundary, coupling via interface shape functions such that consistency conditions are satisfied, bridging domain coupling, compatibility coupling with Lagrange multipliers and hybrid coupling methods where forces from the particles are applied via their shape functions on the FE nodes and vice versa. The hybrid coupling methods are well suited for large deformations and adaptivity and the coupling procedure is independent of the particle distance and nodal arrangement. We will study the methods for several static and dynamic applications, compare the results to analytical and experimental data and show advantages and drawbacks of the methods.

Original languageEnglish
Pages (from-to)1031-1065
Number of pages35
JournalCommunications in Numerical Methods in Engineering
Volume22
Issue number10
DOIs
Publication statusPublished - 2006 Oct 1
Externally publishedYes

Fingerprint

Meshfree Method
Finite Element
Lagrange multipliers
Galerkin methods
Coupling Method
Hydrodynamics
Shape Function
Hybrid Method
Element-free Galerkin Method
Consistency Conditions
Particle Method
Adaptivity
Insulator Elements
Large Deformation
Compatibility
Concepts
Arrangement
Experimental Data
Vertex of a graph

Keywords

  • Adaptivity
  • EFG
  • Mesh-free particle methods
  • SPH

ASJC Scopus subject areas

  • Engineering (miscellaneous)
  • Computational Mechanics
  • Applied Mathematics

Cite this

Coupling of mesh-free methods with finite elements : Basic concepts and test results. / Rabczuk, Timon; Xiao, Shao Ping; Sauer, M.

In: Communications in Numerical Methods in Engineering, Vol. 22, No. 10, 01.10.2006, p. 1031-1065.

Research output: Contribution to journalArticle

Rabczuk, Timon ; Xiao, Shao Ping ; Sauer, M. / Coupling of mesh-free methods with finite elements : Basic concepts and test results. In: Communications in Numerical Methods in Engineering. 2006 ; Vol. 22, No. 10. pp. 1031-1065.
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