The time-dependent Koiter model and its numerical computation

摘要

Highlights•Existence and uniqueness of the time-dependent Koiter model.•Newmark scheme for the time-dependent Koiter model.•Analyses of existence, uniqueness, stability, convergence and priori error estimate for elastodynamic problems.AbstractThe 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.