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 -