Coupling finite element method with meshless finite difference method in thermomechanical problems

This paper focuses on coupling two different computational approaches, namely finite element method (FEM) and meshless finite difference method (MFDM), in one domain. The coupled approach is applied in solving thermomechanical initial–boundary value problem where the heat transport in the domain is...

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Veröffentlicht in:Computers & mathematics with applications (1987) Jg. 72; H. 9; S. 2259 - 2279
Hauptverfasser: Jaśkowiec, J., Milewski, S.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Oxford Elsevier Ltd 01.11.2016
Elsevier BV
Schlagworte:
Approximation
Boundary value problems
Coupling
Coupling approach
Finite difference method
Finite element analysis
Finite element method
Initial value problems
Mathematical analysis
Mathematical models
Mechanical properties
Meshless finite difference method
Meshless methods
Studies
Thermomechanics
Finite element method
Coupling approach
Meshless finite difference method
Thermomechanics
ISSN:0898-1221, 1873-7668
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Zusammenfassung:This paper focuses on coupling two different computational approaches, namely finite element method (FEM) and meshless finite difference method (MFDM), in one domain. The coupled approach is applied in solving thermomechanical initial–boundary value problem where the heat transport in the domain is non-stationary. In this method, the domain is divided into two subdomains for FEM and MFDM, respectively. Contrary to other coupling techniques, the approach presented in this paper is defined in terms of mathematical problem formulation rather than at the approximation level. In the weak form of thermomechanical initial–boundary value problem (variational principle), the appropriate additional coupling integrals are defined a-priori. Subsequently, the FEM and the MFDM approximations, which may differ from each other, are provided to the formulation. It is assumed that there exists a very thin layer of material between the subdomains, which is not spatially discretized. The width of this layer may be considered the coupling parameter and it is the same for both, thermal and mechanical parts. Similar approach is applied to essential boundary conditions (e.g. prescribed temperature and displacements). Consequently, the consistent formulation of the mixed problem for the coupled FEM–MFDM method is derived. The analysis is illustrated with two- and three-dimensional examples of mechanical and thermomechanical problems.
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ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2016.08.020