TY - JOUR
T1 - Variational formulation and symmetric tangent operator for shells with finite rotation field
AU - Suetake, Yoshitaka
AU - Iura, Masashi
AU - Atluri, S. N.
PY - 2003
Y1 - 2003
N2 - The objective of this paper is to examine the symmetry of the tangent operator for nonlinear shell theories with the finite rotation field. As well known, it has been stated that since the rotation field carries the Lie group structure, not a vector space one, the tangent operator incorporating the rotation field does not become symmetric. In this paper, however, it is shown that by adopting a rotation vector as a variable, the symmetry can be achieved in the Lagrangean (material) description. First, we present a general concept for the problem. Next, we adopt the finitely deformed thick shell problem as an example. We also present a tensor formula that plays a key role for the derivation of a symmetric tangent operator.
AB - The objective of this paper is to examine the symmetry of the tangent operator for nonlinear shell theories with the finite rotation field. As well known, it has been stated that since the rotation field carries the Lie group structure, not a vector space one, the tangent operator incorporating the rotation field does not become symmetric. In this paper, however, it is shown that by adopting a rotation vector as a variable, the symmetry can be achieved in the Lagrangean (material) description. First, we present a general concept for the problem. Next, we adopt the finitely deformed thick shell problem as an example. We also present a tensor formula that plays a key role for the derivation of a symmetric tangent operator.
KW - Finite rotation
KW - Shell theory
KW - Symmetry
KW - Tangent operator
KW - Variational formulation
UR - http://www.scopus.com/inward/record.url?scp=8344229956&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:8344229956
SN - 1526-1492
VL - 4
SP - 329
EP - 336
JO - CMES - Computer Modeling in Engineering and Sciences
JF - CMES - Computer Modeling in Engineering and Sciences
IS - 2
ER -