A NOTE ON CONVERGENCE OF LOW ENERGY CRITICAL POINTS OF NONLINEAR ELASTICITY FUNCTIONALS, FOR THIN SHELLS OF ARBITRARY GEOMETRY

作者：Lewicka Marta^*

来源：ESAIM: Control, Optimisation and Calculus of Variations , 2011, 17(2): 493-505.

DOI：10.1051/cocv/2010002

• Shell theories
• nonlinear elasticity
• Gamma convergence
• calculus of variations

We prove that the critical points of the 3d nonlinear elasticity functional on shells of small thickness h and around the mid-surface S of arbitrary geometry, converge as h -> 0 to the critical points of the von Karman functional on S, recently proposed in [Lewicka et al., Ann. Scuola Norm. Sup. Pisa Cl. Sci. (to appear)]. This result extends the statement in [Muller and Pakzad, Comm. Part. Differ. Equ. 33 (2008) 1018-1032], derived for the case of plates when S subset of R(2). The convergence holds provided the elastic energies of the 3d deformations scale like h(4) and the external body forces scale like h(3).

• 出版日期2011-4