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A qualitative accuracy consideration on arch elements
Author(s) -
Yamamoto Yoshiyuki,
Ohtsubo Hideomi
Publication year - 1982
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.1620180806
Subject(s) - finite element method , discretization , arch , a priori and a posteriori , mathematics , stiffness , constant (computer programming) , calculus (dental) , mathematical analysis , computer science , structural engineering , engineering , medicine , philosophy , epistemology , dentistry , programming language
In the present paper, discretization errors in the finite element analysis of arches are investigated quantitatively. So far they have been estimated as an order, such as a power of the element size by means of functional analysis; however, it is insufficient for practical applications, because they depend to a great extent upon the constant of proportionality, which is investigated herein. As a result, it is shown that the constant is affected largely by the arch's stiffness. Errors for displacements are also evaluated with the aid of the energy principle. A formula for a posteriori estimating errors is proposed, which can be evaluated only from the finite element solutions calculated. The validity of the present theory is verified by numerical examples.