On the justification of viscoelastic flexural shell equations

We consider a family of linearly viscoelastic shells of thickness 2 e , all with the same middle surface and fixed on the lateral boundary. By using asymptotic analysis, we find that for external forces of a particular order of e , a two-dimensional viscoelastic flexural shell model is an accurate approximation of the three-dimensional quasistatic problem. Most noticeable is that the limit problem includes a long-term memory that takes into account the previous history of deformations. We provide convergence results which justify our asymptotic approach.