Theory and numerics of thin elastic shells with finite rotations

authored by
F. Gruttmann, E. Stein, Peter Wriggers
Abstract

A bending theory for thin shells undergoing finite rotations is presented, and its associated finite element model is described. The kinematic assumption is based on a Reissner-Mindlin theory. The starting point for the derivation of the strain measures is the polar decomposition of the material deformation gradient. The work-conjugate stress resultants and stress couples are integrals of the Biot stress tensor. This tensor is invariant with respect to rigid body motions and therefore appropriate for the formulation of constitutive equations. The rotations are described by using Eulerian angles. The finite element discretization of arbitrary shells is performed using isoparametric elements. The advantage of the proposed shell formulation and its numerical model is shown by application to different non-linear plate and shell problems. Finite rotations can be calculated within one load increment. Thus the step size of the load increment is only imited by the local convergence behaviour of Newton's method or the appearance of stability phenomena.

Organisation(s)
Institute of Mechanics and Computational Mechanics
Type
Article
Journal
Ingenieur-Archiv
Volume
59
Pages
54-67
No. of pages
14
ISSN
0020-1154
Publication date
01.1989
Publication status
Published
Peer reviewed
Yes
ASJC Scopus subject areas
Engineering(all)
Electronic version(s)
https://doi.org/10.1007/BF00536631 (Access: Unknown)
 

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