Mircea Bîrsan1
Dedicated to the memory of Professsor H. Brezis
Abstract. In the framework of general nonlinear theory of six-parameter shells we derive pointwise necessary conditions for energy minimizers. We consider conservative problems and exploit the property that the sec- ond variation of the potential energy is non-negative if an equilibrium state represents an energy minimizer. Then, using variational calculus we derive the relevant Legendre-Hadamard condition in the theory of shells. Finally, we apply the necessary Legendre-Hadamard inequality to several isotropic strain energy functions proposed previously in the literature on shells.
Keywords: nonlinear 6-parameter shells, Legendre-Hadamard condi- tion, energy minimizers, Cosserat shells, strain energy function.
MSC: 74K25, 74B20, 74G65, 74A60.
DOI 10.56082/annalsarscimath.2025.1.107
1 Faculty of Mathematics, University of Duisburg Essen, Thea-Leymann Str. 9, 45127 Essen, Germany; (2) Octav Mayer Mathematics Institute of the Romanian Academy, Blvd. Carol I, no. 8, 700505 Iasi, Romania mircea.birsan@uni-due.de
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 17 no 1, 2025
