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Deviatoric hybrid model and multivariable elimination at element level for incompressible medium
Author(s) -
Wu ChangChun,
Yuan Lei,
Furukawa Tomonari
Publication year - 1999
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/(sici)1097-0207(19991020)46:5<729::aid-nme695>3.0.co;2-5
Subject(s) - compressibility , element (criminal law) , finite element method , displacement (psychology) , mathematics , stress (linguistics) , incompressible flow , constraint (computer aided design) , set (abstract data type) , mathematical analysis , control theory (sociology) , mechanics , physics , geometry , computer science , structural engineering , engineering , psychology , linguistics , philosophy , control (management) , artificial intelligence , political science , law , psychotherapist , programming language
A deviatoric hybrid element approach, in which the deviatoric stress σ ′, the pressure p and the displacement u are independently dealt with as the element variables, is suggested. The present approach is naturally universal for compressible and fully incompressible mediums. Moreover, it can be extended to the simulation of Stokes flow directly. The resulting hybrid model is able to meet the zero volumetric strain constraint in terms of the incompatible displacement mode only. Therefore an incompressible elimination can be carried out within an individual element, and the complex system elimination for nodal displacements is then avoided. The present 3‐field hybrid model maintains the important features of current hybrid stress elements—finally resulting in a set of displacement‐type discrete equations which can be easily solved, while not a set of u ‐ p mixed‐type equations resulted. Regarding the numerical stability of the element, an effective strategy is offered to suppress all the zero energy modes hidden in the model. Copyright © 1999 John Wiley & Sons, Ltd.