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

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, c...

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Veröffentlicht in:	Communications in numerical methods in engineering Jg. 22; H. 10; S. 1031 - 1065
Hauptverfasser:	Rabczuk, T., Xiao, S. P., Sauer, M.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Chichester, UK John Wiley & Sons, Ltd 01.10.2006 Wiley
Schlagworte:	adaptivity Boundaries Computational techniques Consistency Dynamic tests EFG Exact sciences and technology Finite element method Fundamental areas of phenomenology (including applications) Joining Mathematical analysis Mathematical methods in physics mesh-free particle methods Meshless methods Physics Shape functions SPH High strain Smoothed particle hydrodynamics method EFG Master slave relationship SPH Experimental study Finite element method Crack bridging Lagrange multiplier Particle method adaptivity Granular materials Meshless method Modelling Least square fit mesh-free particle methods
ISSN:	1069-8299, 1099-0887
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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. Copyright © 2006 John Wiley & Sons, Ltd.
AbstractList	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. 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. Copyright © 2006 John Wiley & Sons, Ltd.
Author	Xiao, S. P. Rabczuk, T. Sauer, M.
Author_xml	– sequence: 1 givenname: T. surname: Rabczuk fullname: Rabczuk, T. email: Timon.Rabczuk@lnm.mur.tum.de organization: Institute for Numerical Mechanics, University of Munich, Garching, Germany – sequence: 2 givenname: S. P. surname: Xiao fullname: Xiao, S. P. email: shaoping-xiao@uiowa.edu organization: Department of Mechanical and Industrial Engineering, University of Iowa, Iowa City, U.S.A – sequence: 3 givenname: M. surname: Sauer fullname: Sauer, M. email: sauer@emi.fhg.de organization: Fraunhofer Institute for Short Time Dynamics, Ernst-Mach-Institute, Eckerstrasse 4, 79106 Freiburg, Germany
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Keywords	High strain Smoothed particle hydrodynamics method EFG Master slave relationship SPH Experimental study Finite element method Crack bridging Lagrange multiplier Particle method adaptivity Granular materials Meshless method Modelling Least square fit mesh-free particle methods
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Snippet	This paper reviews several novel and older methods for coupling mesh‐free particle methods, particularly the element‐free Galerkin (EFG) method and the smooth... This paper reviews several novel and older methods for coupling mesh-free particle methods, particularly the element-free Galerkin (EFG) method and the smooth...
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SubjectTerms	adaptivity Boundaries Computational techniques Consistency Dynamic tests EFG Exact sciences and technology Finite element method Fundamental areas of phenomenology (including applications) Joining Mathematical analysis Mathematical methods in physics mesh-free particle methods Meshless methods Physics Shape functions SPH
Title	Coupling of mesh-free methods with finite elements: basic concepts and test results
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