A Linear Isotropic Cosserat Shell Model Including Terms up to $O(h^{5})$. Existence and Uniqueness

On the Equilibrium Equations of Linear 6-Parameter Elastic Shells

“…In the last section, we show that this general existence theorem can be applied in the case of isotropic and higher-order 6-parameter shell models. In this way, we obtain existence results for isotropic linear 6-parameter shells which improve and complement the available results presented in the literature [12,16,17].…”

“…The existence of weak solutions for a related linear Cosserat shell model of order O(h 3 ) has been established previously in [17]. Notice that Corollary 2 is an improvement of the existence theorem presented in [17], in the sense that the hypotheses on the coefficients (94) are less restrictive and the conditions (95) have been optimized.…”

“…Let (u, w) be a classical solution of the boundary-value problem for linearly elastic 6-parameter shells, which consists in the equilibrium equations (28), the boundary conditions (29), the geometrical relations ( 15), (17), and the constitutive equations (42).…”

“…where the tensors e and k are expressed in terms of (u, w) by the geometrical relations ( 15), (17).…”

“…Recently, a higher-order nonlinear model for 6-parameter shells made of isotropic Cosserat material has been established and analyzed in [13,14,15]. Then, the linearized model for such isotropic 6-parameter Cosserat shells has been presented in [16,17], where the existence and uniqueness of weak solutions is proved. In the present work, we derive the linearized equations of general (anisotropic) 6-parameter shells and show an existence result.…”