Details
| Original language | English |
|---|---|
| Pages (from-to) | 54-67 |
| Number of pages | 14 |
| Journal | Ingenieur-Archiv |
| Volume | 59 |
| Issue number | 1 |
| Publication status | Published - Jan 1989 |
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.
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In: Ingenieur-Archiv, Vol. 59, No. 1, 01.1989, p. 54-67.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Theory and numerics of thin elastic shells with finite rotations
AU - Gruttmann, F.
AU - Stein, E.
AU - Wriggers, Peter
PY - 1989/1
Y1 - 1989/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0024866558&partnerID=8YFLogxK
U2 - 10.1007/BF00536631
DO - 10.1007/BF00536631
M3 - Article
AN - SCOPUS:0024866558
VL - 59
SP - 54
EP - 67
JO - Ingenieur-Archiv
JF - Ingenieur-Archiv
SN - 0020-1154
IS - 1
ER -