TY - JOUR
T1 - Intrinsic Formulation of the Kirchhoff-Love Theory of Nonlinearly Elastic Shallow Shells
AU - Ciarlet , Philippe G.
AU - Mardare , Cristinel
JO - Communications in Mathematical Analysis and Applications
VL - 4
SP - 545
EP - 567
PY - 2022
DA - 2022/10
SN - 1
DO - http://doi.org/10.4208/cmaa.2022-0017
UR - https://global-sci.org/intro/article_detail/cmaa/21121.html
KW - Nonlinearly elastic shallow shells, displacement-traction problem, Kirchhoff-Love theory, Saint-Venant compatibility conditions, Euler-Lagrange equation, intrinsic formulation.
AB - <p style="text-align: justify;">The classical formulation of the Kirchhoff-Love theory of nonlinearly
elastic shallow shells consists of a system of nonlinear partial differential equations and boundary conditions whose unknowns are the Cartesian components
of the displacement field of the middle surface of the shell subjected to applied forces. We show that this system is equivalent to a system whose sole
unknowns are the bending moments and stress resultants inside the middle
surface of the shell. This system thus provides a direct method for computing
the stresses appearing in such a shell, without any recourse to the displacement
field. To this end, we first establish specific compatibility conditions of Saint-Venant type for the bending moments and stress resultants; we then identify
the boundary conditions that these fields must satisfy.</p>