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Plane isoparametric hybrid‐stress elements: Invariance and optimal sampling
Author(s) -
Spilker R. L.,
Maskeri S. M.,
Kania E.
Publication year - 1981
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.1620171004
Subject(s) - finite element method , mathematics , spurious relationship , plane stress , compatibility (geochemistry) , invariant (physics) , elasticity (physics) , mathematical analysis , rotational invariance , geometry , structural engineering , algorithm , engineering , physics , statistics , chemical engineering , mathematical physics , thermodynamics
Formulation and applications of the hybrid‐stress finite element model to plane elasticity problems are examined. Conditions for invariance of the element stiffness are established for two‐dimensional problems, the results of which are easily extended to three‐dimensional cases. Next, the hybrid‐stress functional for a 3‐D continuum is manipulated into a more convenient form in which the location of optimal stress/strain sampling points can be identified. To illustrate these concepts, 4‐ and 8‐node plane isoparametric hybrid‐stress elements which are invariant and of correct rank are developed and compared with existing hybrid‐stress elements. For a 4‐node element, lack of invariance is shown to lead to spurious zero energy modes under appropriate element rotation. Alternative 8‐node elements are considered, and the best invariant element is shown to be one in which the stress compatibility equations are invoked. Results are also presented which demonstrate the validity of the optimal sampling points, the effects of reduced orders of numerical integration, and the behaviour of the elements for nearly incompressible materials.