Families of 4-node and 9-node finite elements for a finite deformation shell theory. An assesment of hybrid stress, hybrid strain and enhanced strain elements |
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Authors: | C Sansour F G Kollmann |
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Affiliation: | Institut für Baustatik, Universit?t Karlsruhe, Kaiserstr. 12, 76131 Karlsruhe, Germany, DE Darmstadt University of Technology, Fachgebiet Maschinenelemente und Akustik, Magdalenenstr. 4, 64289 Darmstadt, Germany, DE
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Abstract: | In this paper we discuss and compare three types of 4-node and 9-node finite elements for a recently formulated finite deformation
shell theory with seven degrees of freedom. The shell theory takes thickness change into account and circumvents the use of
a rotation tensor. It allows for the applicability of three-dimensional constitutive laws and equipes the configuration space
with the structure of a vector space. The finite elements themselves are based either on a hybrid stress functional, on a
hybrid strain functional, or on a nonlinear version of the enhanced strain concept. As independent variables either the normal
and shear resultants, the strain tensor related to the deformation of the midsurface, or the incompatible enhanced strain
field are taken as independent variables. The fields of equivalence of these different formulations, their limitations as
well as possible improvements are discussed using different numerical examples.
Received 10 December 1998 |
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