TY - JOUR
T1 - Asymptotic models for curved rods derived from nonlinear elasticity by Gamma-convergence
AU - Scardia, L.
PY - 2009
Y1 - 2009
N2 - We study the problem of the rigorous derivation of one-dimensional models for a thin curved beam starting from three-dimensional nonlinear elasticity. We describe the limiting models obtained for different scalings of the energy. In particular, we prove that the limit functional corresponding to higher scalings coincides with the one derived by dimension reduction starting from linearized elasticity. Finally we also address the case of thin elastic rings
AB - We study the problem of the rigorous derivation of one-dimensional models for a thin curved beam starting from three-dimensional nonlinear elasticity. We describe the limiting models obtained for different scalings of the energy. In particular, we prove that the limit functional corresponding to higher scalings coincides with the one derived by dimension reduction starting from linearized elasticity. Finally we also address the case of thin elastic rings
U2 - 10.1017/S0308210507000194
DO - 10.1017/S0308210507000194
M3 - Article
VL - 139
SP - 1037
EP - 1070
JO - Proceedings of the Royal Society of Edinburgh Section A : Mathematics
JF - Proceedings of the Royal Society of Edinburgh Section A : Mathematics
SN - 0308-2105
ER -