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Influence functions and goal‐oriented error estimation for finite element analysis of shell structures
Author(s) -
Grätsch Thomas,
Bathe KlausJürgen
Publication year - 2005
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.1298
Subject(s) - finite element method , shell (structure) , function (biology) , mathematics , focus (optics) , domain (mathematical analysis) , element (criminal law) , error analysis , computer science , mathematical optimization , algorithm , calculus (dental) , mathematical analysis , engineering , structural engineering , mechanical engineering , physics , medicine , dentistry , optics , evolutionary biology , political science , law , biology
In this paper, we first present a consistent procedure to establish influence functions for the finite element analysis of shell structures, where the influence function can be for any linear quantity of engineering interest. We then design some goal‐oriented error measures that take into account the cancellation effect of errors over the domain to overcome the issue of over‐estimation. These error measures include the error due to the approximation in the geometry of the shell structure. In the calculation of the influence functions we also consider the asymptotic behaviour of shells as the thickness approaches zero. Although our procedures are general and can be applied to any shell formulation, we focus on MITC finite element shell discretizations. In our numerical results, influence functions are shown for some shell test problems, and the proposed goal‐oriented error estimation procedure shows good effectivity indices. Copyright © 2005 John Wiley & Sons, Ltd.