Thin shells with finite rotations formulated in biot stresses

Theory and finite element formulation

authored by: Peter Wriggers, F. Gruttmann
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 shear elastic Reissner‐Mindlin theory. The starting point for the derivation of the strain measures are the resultant equilibrium equations and the associated principle of virtual work. Within this formulation the polar decomposition of the shell material deformation gradient leads to symmetric strain measures. The associated 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. Finite rotations are introduced via Eulerian angles. The finite element discretization of arbitrary shells is based on the isoparametric concept formulated with respect to a plane reference configuration. The numerical model is applied to different non‐linear plate and shell problems and compared with existing formulations. Due to a consistent linearization, the step size of a load increment is only limited by the local convergence behaviour of Newton's method.
External Organisation(s): Technische Universität Darmstadt
Type: Article
Journal: International Journal for Numerical Methods in Engineering
Volume: 36
Pages: 2049-2071
No. of pages: 23
ISSN: 0029-5981
Publication date: 30.06.1993
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Numerical Analysis, Engineering(all), Applied Mathematics
Electronic version(s): https://doi.org/10.1002/nme.1620361207 (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{648416fdf9b24e9d953bfb08960ab600,
title = "Thin shells with finite rotations formulated in biot stresses: Theory and finite element formulation",
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 shear elastic Reissner‐Mindlin theory. The starting point for the derivation of the strain measures are the resultant equilibrium equations and the associated principle of virtual work. Within this formulation the polar decomposition of the shell material deformation gradient leads to symmetric strain measures. The associated 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. Finite rotations are introduced via Eulerian angles. The finite element discretization of arbitrary shells is based on the isoparametric concept formulated with respect to a plane reference configuration. The numerical model is applied to different non‐linear plate and shell problems and compared with existing formulations. Due to a consistent linearization, the step size of a load increment is only limited by the local convergence behaviour of Newton's method.",
author = "Peter Wriggers and F. Gruttmann",
year = "1993",
month = jun,
day = "30",
doi = "10.1002/nme.1620361207",
language = "English",
volume = "36",
pages = "2049--2071",
journal = "International Journal for Numerical Methods in Engineering",
issn = "0029-5981",
publisher = "John Wiley and Sons Ltd",
number = "12",
}