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Quadrature rules for brick based finite elements
Author(s) -
Irons Bruce M.
Publication year - 1971
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.1620030213
Subject(s) - brick , citation , library science , computer science , engineering , information retrieval , civil engineering
Already isoparametric hexahedral (brick) finite elements with 20 or 32 nodes1 are highly com petitive in practice, despite the observation that 50 per cent of the total computation is often absorbed in numerically integrating the coefficients of the equations.2 This cost is approximately halved3 by a method based, essentially, on using a 9 x 9 [D] matrix which operates on iu/ox, ou/oy, ou/cz, ot•/c1x, ... ow/oz-a technique which, moreover, is more general than the classical S BT DB x constant algorithm.4 The purpose of this note is to demonstrate how one may further halve the cost by using simpler integration formulae having the same order of truncation error. We compare certain Gaussian type rules, some of them new and all of them designed to integrate complete polynomials, with the corresponding product-Gauss rules which are normally used.5 The former integrate correctly