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Mixed models and reduced/selective integration displacement models for nonlinear analysis of curved beams
Author(s) -
Noor Ahmed K.,
Peters Jeanne M.
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.1620170409
Subject(s) - arch , nonlinear system , mathematics , mathematical analysis , displacement (psychology) , finite element method , transverse plane , equivalence (formal languages) , geometry , structural engineering , physics , engineering , psychology , discrete mathematics , quantum mechanics , psychotherapist
Simple mixed models are developed for the geometrically nonlinear analysis of deep arches. A total Lagrangian description of the arch deformation is used and the analytical formulation is based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included. The fundamental unknowns consist of the six internal forces and generalized displacements of the arch, and the element characteristic arrays are obtained by using Hellinger–Reissner mixed variational principle. The polynomial interpolation functions used in approximating the forces are one degree lower than those used for approximating the displacements, and the forces are discontinuous at the interelement boundaries. The equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms is discussed. The advantages of mixed models over equivalent displacement models are outlined. Numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed, and compare their performance with other mixed models reported in the literature.