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A three‐dimensional finite element method with arbitrary polyhedral elements
Author(s) -
Rashid M. M.,
Selimotic M.
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.1625
Subject(s) - finite element method , polygon mesh , mixed finite element method , extended finite element method , convergence (economics) , mathematics , hp fem , kinematics , displacement (psychology) , smoothed finite element method , topology (electrical circuits) , finite element limit analysis , mesh generation , degrees of freedom (physics and chemistry) , mathematical analysis , geometry , structural engineering , boundary knot method , classical mechanics , engineering , physics , psychology , combinatorics , quantum mechanics , boundary element method , economics , psychotherapist , economic growth
Abstract The ‘variable‐element‐topology finite element method’ (VETFEM) is a finite‐element‐like Galerkin approximation method in which the elements may take arbitrary polyhedral form. A complete development of the VETFEM is given here for both two and three dimensions. A kinematic enhancement of the displacement‐based formulation is also given, which effectively treats the case of near‐incompressibility. Convergence of the method is discussed and then illustrated by way of a 2D problem in elastostatics. Also, the VETFEM's performance is compared to that of the conventional FEM with eight‐node hex elements in a 3D finite‐deformation elastic–plastic problem. The main attraction of the new method is its freedom from the strict rules of construction of conventional finite element meshes, making automatic mesh generation on complex domains a significantly simpler matter. Copyright © 2006 John Wiley & Sons, Ltd.