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A finite element tensor approach to plate buckling and postbuckling
Author(s) -
Vos Robert G.,
Vann William P.
Publication year - 1973
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.1620050306
Subject(s) - buckling , finite element method , convergence (economics) , mathematics , tensor (intrinsic definition) , relaxation (psychology) , dynamic relaxation , strain energy , mixed finite element method , mathematical analysis , structural engineering , geometry , engineering , psychology , social psychology , economics , economic growth
Abstract A practical finite element method is presented for geometrically non‐linear (von Kármán) plate problems. Symmetric strain energy tensors provide an efficient formulation and solution, and allow the effects of initial imperfections to be considered. An unbalanced force iteration is employed, with the advantage that the time consuming Gauss decomposition needs to be performed only once. The convergence is controlled by an automatically computed relaxation factor, and this makes the method applicable in advanced stage of non‐linearity. Several different triangular elements are used in explicitly the required tensors. Buckling and post‐buckling solutions are outlined and demonstrated by numerical examples.