M. Bîrsan†
Abstract: We consider the linearized theory of 6-parameter elastic shells with general anisotropy. We derive the equilibrium equations from the virtual power statement and formulate the corresponding variational problem in the suitable functional framework. Then, using a Korn-type inequality for the linearized strain measures we prove the existence and uniqueness of weak solutions. Finally, we show that our general theorem can be applied to obtain existence results in the case of isotropic elastic shells. We illustrate this procedure by investigating three different linear shell models established previously in the literature, namely the simplified isotropic 6-parameter shell, the Cosserat isotropic model, and the higher-order 6-parameter Cosserat model.
MSC: 74K25, 74B15, 74A05, 74A60, 74G65.
keywords: linear elastic shells, 6-parameter shells, Cosserat model, weak solutions, existence and uniqueness
DOI 10.56082/annalsarscimath.2023.1-2.94
†mircea.birsan@uni-due.de Faculty of Mathematics, University Duisburg-Essen, Thea-Leymann Str. 9, 45127 Essen, Germany; and Institute of Mathematics Octav Mayer of the Romanian Academy, Blvd. Carol I, no. 8, 700505 Ia¸si, Romania.
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 15 no 1-2, 2023
