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A finite element model for shells based on the discrete Kirchhoff hypothesis
Author(s) -
Weeks George E.
Publication year - 1972
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.1620050102
Subject(s) - finite element method , conical surface , extension (predicate logic) , bending , shell (structure) , displacement field , mathematics , field (mathematics) , rotational symmetry , displacement (psychology) , deformation (meteorology) , mathematical analysis , geometry , structural engineering , engineering , physics , computer science , mechanical engineering , psychology , meteorology , pure mathematics , psychotherapist , programming language
A ring type finite element model based on the discrete Kirchhoff hypothesis is developed and its feasibility for use in shell analysis is illustrated by determining the linear axisymmetric deformation behaviour of a conical shell loaded by lateral pressure. The displacement field is represented by a linear function of the meridional co‐ordinate. The effects of coupling between bending and extension are included and in this respect the analysis is an extension of earlier work by other investigators using this same model, where bending deformations only were considered. The results of the investigation indicate that the proposed model is capable of accurately described coupled bending and extension effects with a relatively small number of elements. In addition to the numerical results obtained several distinct advantages and disadvantages of this element are brought out. In particular, the element stiffness coefficients can be easily derived because of the simplicity of the assumed vector field. However, it appears that the price paid for such a simple vector field approximation is an undue amount of machine storage, even for a relatively small number of elements. Several suggestions are made for minimizing some of these difficulties.