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

VL - 4

SP - 329

EP - 336

JO - CMES - Computer Modeling in Engineering and Sciences

JF - CMES - Computer Modeling in Engineering and Sciences

SN - 1526-1492

IS - 2

ER -