scholarly journals Existence theorem for a first-order Koiter nonlinear shell model

2019 ◽  
Vol 12 (6) ◽  
pp. 1535-1545
Author(s):  
Sylvia Anicic ◽  
Keyword(s):  
Shell Model ◽  
Existence Theorem ◽  
First Order ◽  
Nonlinear Shell

scholarly journals A nonlinear shell model of Koiter's type

2018 ◽  
Vol 356 (2) ◽  
pp. 227-234 ◽  
Author(s):  
Philippe G. Ciarlet ◽  
Cristinel Mardare
Keyword(s):  
Shell Model ◽  
Nonlinear Shell

JUSTIFICATION OF A TWO-DIMENSIONAL NONLINEAR SHELL MODEL OF KOITER'S TYPE

2001 ◽  
Vol 22 (02) ◽  
pp. 129-144 ◽  
Author(s):  
P. G. CIARLET ◽  
A. ROQUEFORT
Keyword(s):  
Shell Model ◽  
Two Dimensional ◽  
Nonlinear Shell

An existence theorem for a two-dimensional nonlinear shell model of Koiter’s type

2018 ◽  
Vol 28 (14) ◽  
pp. 2833-2861 ◽  
Author(s):  
Philippe G. Ciarlet ◽  
Cristinel Mardare
Keyword(s):  
Shell Model ◽  
Energy Function ◽  
Vector Fields ◽  
Elastic Shell ◽  
Existence Theory ◽  
Specific Class ◽  
Two Dimensional ◽  
Stored Energy ◽  
Nonlinear Shell ◽  
Order Part

We propose a minimization problem with a stored energy function that is polyconvex and satisfies all the other assumptions of John Ball’s theorem, while being at the same time well adapted for modeling a nonlinearly elastic shell. By restricting the admissible deformations to be specific quadratic polynomials with respect to the transverse variable, we are able to define a new nonlinear shell model for which a satisfactory existence theory is available and that is still two-dimensional, in the sense that minimizing the corresponding total energy amounts to finding three vector fields defined on the closure of a bounded open subset of [Formula: see text]. The most noteworthy feature of our nonlinear shell model is that the “lowest order part” of its stored energy function coincides, at least formally, with the stored energy function found in Koiter’s model for a specific class of deformations that are to within the first-order identical to the Kirchhoff–Love deformations considered by W. T. Koiter.

Sign in / Sign up

Export Citation Format

Share Document