Spline approximation of thin shell dynamics

A spline-based method for approximating thin shell dynamics is presented here. While the method is developed in the context of the DonnellÐMushtari thin shell equations, it can be easily extended to the ByrneÐFlu¬ ggeÐLurÕye equations or other models for shells of revolution as warranted by applications. The primary requirements for the method include accuracy, ßexibility and e¦ciency in smart material applications. To accomplish this, the method was designed to be ßexible with regard to boundary conditions, material non-homogeneities due to sensors and actuators, and inputs from smart material actuators such as piezoceramic patches. The accuracy of the method was also of primary concern, both to guarantee full resolution of structural dynamics and to facilitate the development of PDE-based controllers which ultimately require real-time implementation. Several numerical examples provide initial evidence demonstrating the e¦cacy of the method