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An improved stress recovery technique for low‐order 3D finite elements
Author(s) -
Sharma Rahul,
Zhang Jian,
Langelaar Matthijs,
Keulen Fred,
Aragón Alejandro M.
Publication year - 2018
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.5734
Subject(s) - finite element method , stress field , rate of convergence , stress (linguistics) , elasticity (physics) , displacement field , displacement (psychology) , convergence (economics) , mathematics , linear elasticity , stress space , field (mathematics) , sense (electronics) , mathematical optimization , mathematical analysis , structural engineering , computer science , engineering , materials science , pure mathematics , composite material , electrical engineering , psychology , computer network , channel (broadcasting) , linguistics , philosophy , constitutive equation , economics , psychotherapist , economic growth
Summary In this paper, we propose a stress recovery procedure for low‐order finite elements in 3D. For each finite element, the recovered stress field is obtained by satisfying equilibrium in an average sense and by projecting the directly calculated stress field onto a conveniently chosen space. Compared with existing recovery techniques, the current procedure gives more accurate stress fields, is simpler to implement, and can be applied to different types of elements without further modification. We demonstrate, through a set of examples in linear elasticity, that the recovered stresses converge at a higher rate than that of directly calculated stresses and that, in some cases, the rate of convergence is the same as that of the displacement field.