TY - JOUR
T1 - The matching property of infinitesimal isometries on elliptic surfaces and elasticity on thin shells
JF - Archive for Rational Mechanics and Analysis 200 (2011) 1023-1050
Y1 - 2011
A1 - Marta Lewicka
A1 - Maria Giovanna Mora
A1 - Mohammad Reza Pakzad
AB - Using the notion of Γ-convergence, we discuss the limiting behavior of the three-dimensional nonlinear elastic energy for thin elliptic shells, as their thickness h converges to zero, under the assumption that the elastic energy of deformations scales like h β with 2 < β < 4. We establish that, for the given scaling regime, the limiting theory reduces to linear pure bending. Two major ingredients of the proofs are the density of smooth infinitesimal isometries in the space of W 2,2 first order infinitesimal isometries, and a result on matching smooth infinitesimal isometries with exact isometric immersions on smooth elliptic surfaces.
PB - Springer
UR - http://hdl.handle.net/1963/3392
U1 - 940
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Shell theories arising as low energy Gamma-limit of 3d nonlinear elasticity
JF - Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. IX (2010) 253-295
Y1 - 2010
A1 - Marta Lewicka
A1 - Maria Giovanna Mora
A1 - Mohammad Reza Pakzad
AB - We discuss the limiting behavior (using the notion of gamma-limit) of the 3d nonlinear elasticity for thin shells around an arbitrary smooth 2d surface. In particular, under the assumption that the elastic energy of deformations scales like h4, h being the thickness of a shell, we derive a limiting theory which is a generalization of the von Karman theory for plates.
UR - http://hdl.handle.net/1963/2601
U1 - 1521
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - A nonlinear theory for shells with slowly varying thickness
JF - C. R. Math. 347 (2009) 211-216
Y1 - 2009
A1 - Marta Lewicka
A1 - Maria Giovanna Mora
A1 - Mohammad Reza Pakzad
AB - We study the Γ-limit of 3d nonlinear elasticity for shells of small, variable thickness, around an arbitrary smooth 2d surface.
UR - http://hdl.handle.net/1963/2632
U1 - 1491
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -