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Closed form elastic‐plastic stiffness matrix for axisymmetric finite elements
Author(s) -
Rich T. P.
Publication year - 1978
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.1620120106
Subject(s) - finite element method , rotational symmetry , stiffness matrix , stiffness , von mises yield criterion , direct stiffness method , mathematics , plasticity , mathematical analysis , structural engineering , geometry , mechanics , physics , engineering , thermodynamics
This note presents the closed form equations for the stiffness terms in the elastic‐plastic stiffness matrix for axisymmetric finite elements. The element considered is a triangular ring element characterized by linear displacement relationships and an averaged state of stress. The physical law is modelled by the incremental theory of plasticity utilizing the Prandtl‐Reuss flow rule and von‐Mises Yield Criterion. Results are presented comparing stiffness terms as computed by numerical integration to those computed from the closed form equations. Significant errors in stiffness terms arising from numerical integration are observed for axisymmetric elements located near the line of axial symmetry as a result of the logarithmic nature of some of the stiffness terms.