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Fraeijs de Veubeke variational principle‐based cylindrical shell finite element model
Author(s) -
Kocsán Lajos György
Publication year - 2013
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201310047
Subject(s) - shell (structure) , variational principle , tensor (intrinsic definition) , finite element method , cauchy stress tensor , a priori and a posteriori , mathematical analysis , constitutive equation , mathematics , classical mechanics , physics , geometry , materials science , thermodynamics , philosophy , epistemology , composite material
In this paper a dimensionally reduced cylindrical shell model based on the dual‐mixed variational principle of Fraeijs de Veubeke will be presented. The fundamental variables of this variational principle are the not a priori symmetric stress tensor and the skew‐symmetric rotation tensor. The tensor of first‐order stress functions is applied to satisfy translational equilibrium. A shell model derived in this way makes the application of the classical kinematical hypotheses unnecessary, and enables us to use unmodified three‐dimensional constitutive equations. On the basis of this shell model, a new dual‐mixed cylindrical shell finite elements capable of both h ‐ and p ‐approximation can be derived. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)