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New findings on limit state analysis with unstructured triangular finite elements
Author(s) -
Preisig M.,
Prévost J. H.
Publication year - 2013
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.4455
Subject(s) - finite element method , limit (mathematics) , interpolation (computer graphics) , limit load , discontinuous galerkin method , polygon mesh , galerkin method , computer science , mathematics , overshoot (microwave communication) , stress (linguistics) , mesh generation , mathematical optimization , structural engineering , geometry , mathematical analysis , engineering , animation , telecommunications , linguistics , philosophy , computer graphics (images)
SUMMARY The emergence of high performance unstructured mesh generators enables the use of low‐order triangles and tetrahedras for a wide variety of problems, where no structured quadrangular mesh can be easily constructed. Some of the results acknowledged by the community of computational mechanics therefore need to be carefully looked at under the light of these recent advances in unstructured and adaptive meshing. In particular, we question evidence of locking during plastic flow, as it has been presented by several authors in the past. We claim that locking can also manifest through stress oscillations. Overshoot of limit loads or displacement locking can be explained by other causes: Insufficient mesh refinement or comparison with analytical solutions that are based on assumptions that are inconsistent with the finite element model. We present a stabilized Galerkin mixed method that allows accurate and converging limit loads to be computed for any elastic‐plastic problem using standard equal‐order interpolation for both displacements and mean stress for low‐order linear triangular elements. The method is attractive for simulations where the cost of meshing is more important than the added computational cost of an additional nodal unknown required by the mixed formulation. Copyright © 2013 John Wiley & Sons, Ltd.