TY - JOUR
T1 - Existence Theorem for a Nonlinear Elliptic Shell Model
AU - BUNOIU, Renata
AU - CIARLET, Philippe G.
AU - MARDARE, Cristinel
PY - 2015/4
Y1 - 2015/4
N2 - In this paper we introduce a new nonlinear shell model with the following properties. First, we show that, if the middle surface of the undeformed shell is elliptic, then this new nonlinear shell model possesses solutions which are also elliptic surfaces. Second, we show that, if in addition the middle surface of the undeformed shell is a portion of a sphere, then the total energy of this nonlinear shell model coincides to within the first order, i.e., for “small enough” change of metric and change of curvature tensors, with the total energy of the well-known Koiter nonlinear shell model.
AB - In this paper we introduce a new nonlinear shell model with the following properties. First, we show that, if the middle surface of the undeformed shell is elliptic, then this new nonlinear shell model possesses solutions which are also elliptic surfaces. Second, we show that, if in addition the middle surface of the undeformed shell is a portion of a sphere, then the total energy of this nonlinear shell model coincides to within the first order, i.e., for “small enough” change of metric and change of curvature tensors, with the total energy of the well-known Koiter nonlinear shell model.
KW - Nonlinear shell theory
KW - Calculus of variations
KW - Polyconvexity
UR - http://www.scopus.com/inward/record.url?scp=84996589659&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84996589659&origin=recordpage
U2 - 10.1007/BF03377366
DO - 10.1007/BF03377366
M3 - RGC 21 - Publication in refereed journal
SN - 2296-9020
VL - 1
SP - 31
EP - 48
JO - Journal of Elliptic and Parabolic Equations
JF - Journal of Elliptic and Parabolic Equations
IS - 1
ER -