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A refined curved element for thin shells of revolution
Author(s) -
Popov E. P.,
Sharifi P.
Publication year - 1971
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.1620030405
Subject(s) - classification of discontinuities , stress resultants , rotational symmetry , finite element method , curvature , cartesian coordinate system , shell (structure) , geometry , zonal and meridional , degrees of freedom (physics and chemistry) , plane (geometry) , mathematics , mathematical analysis , physics , structural engineering , materials science , engineering , atmospheric sciences , quantum mechanics , composite material
A refined axisymmetric curved finite element for the analysis of thin elastic‐plastic shells of revolution is described in the paper. The improved element is obtained by employing cubic polynomials in terms of local Cartesian co‐ordinates for the assumed in‐plane and out‐of‐plane displacements. This introduces into the solution two internal degrees of freedom in the cord direction of each element. These internal degrees of freedom are removed by static condensation before assembling the individual element stiffness matrices, and are subsequently recovered after the nodal displacements are obtained. On comparison with the previous formulation, this procedure greatly improves the accuracy of the solution especially with regards to in‐plane stress‐resultants at discontinuities in the meridional curvature and interelement equilibrium of forces. The latter fact makes it possible to analyse shells with a discontinuous meridional slope. In using this element, improvement in the convergence of the elastic‐plastic solutions has also been observed. Several examples illustrate the quality of solutions. The reported study is limited to axisymmetric loadings cum boundary conditions.