Premium
A large‐strain elasto–plastic shell formulation using the Morley triangle
Author(s) -
Kolahi A. S.,
Crisfield M. A.
Publication year - 2001
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.232
Subject(s) - mathematics , multiplicative function , invariant (physics) , rotation (mathematics) , plasticity , constraint (computer aided design) , geometry , mathematical analysis , physics , mathematical physics , thermodynamics
Abstract The paper describes a large‐strain elasto–plastic formulation for shells, which is based on the faceted ‘Morley triangle’, with rotation variables only being provided at each mid‐side in the form of a rotation about the side.A co‐rotational formulation is adopted, with the local deformation gradient being obtained from a polar decomposition using F = RU . The material description is then based around ‘log e U ’, with U being decomposed into principal directions. Plasticity is treated with the aid of the multiplicative F = F e F p . In contrast to many earlier formulations with the Morley triangle, the current formulation is invariant to the node numbering. In order to achieve this invariance, it is necessary to re‐visit the origins of the Morley triangle and to re‐cast the formulation as a special form of ‘discrete‐Kirchhoff approach’. The associated constraint is now applied in relation to the ‘current configuration’. Copyright © 2001 John Wiley & Sons, Ltd.