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An analysis of alternatives for computing axisymmetric element stiffness matrices
Author(s) -
Palacios Jose Antonio,
Henriksen Mogens
Publication year - 1982
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.1620180114
Subject(s) - numerical integration , finite element method , quadrature (astronomy) , stiffness matrix , gaussian quadrature , mathematics , stiffness , rotational symmetry , mathematical analysis , direct stiffness method , computation , displacement (psychology) , integrator , matrix (chemical analysis) , geometry , structural engineering , computer science , physics , algorithm , engineering , nyström method , materials science , psychotherapist , optics , integral equation , psychology , computer network , bandwidth (computing) , composite material
This note compares the use of numerical and closed form integration in computation of element stiffness matrices for axisymmetric finite element analysis. Only constant strain elements are considered. Results obtained with Gaussian quadrature and closed form integrators are compared mutually and with an exact solution obtained from classical methods. The FEM global equations estimate the force‐displacement behaviour of an elastic continuum with an accuracy that depends on the integration method used. Selection of an integration order minimizing error is particularly critical in the presence of high stress gradients. Best results in the vicinity of the axis of revolution may be obtained with single‐point integration rather than higher order approximations or exact integration of the element stiffness matrix. This phenomenon and its consequences are subsequently discussed.