Existence and uniqueness of solutions to the dynamic equations for Koiter shells (Q1818189)

The author considers family of linear elastic shells of thickness \(2\varepsilon\) with the same middle surface \(S=\varphi (\overline \omega) \subset \mathbb{R}^3\), \(\omega\subset \mathbb{R}^2\) is a bounded and connected open set with Lipschitz-continuous boundary, \(\varphi\in C^3(\overline \omega; \mathbb{R}^3)\). The shells are clamped on a portion of their lateral face, whose middle line is \(\varphi (\gamma_0)\), \(\gamma_0\) is a portion of \(\partial\omega\) with length \(\gamma_0 >0\). The two-dimensional dynamic Koiter model is studied by Galerkin method, and the existence and uniqueness of solutions are proved.