The time-dependent Koiter model and its numerical computation

The theory of elastic shells is one of the most important branches of the theory of elasticity. Among all the shell models, a classical and widely recognized model is the Koiter model. In this paper, we discuss the time-dependent Koiter model, which has not been addressed numerically. We show that the solution of this model exists and is unique. We semi-discretize the space variable and fully discretize the problem using the time discretization by the Newmark scheme. The corresponding analyses of existence, uniqueness, stability, convergence and a priori error estimate are given. Finally, we provide numerical experiments with a portion of spherical shell and a portion of cylindrical shell to demonstrate the efficiency of the model.