On the Free Boundary Conditions for a Dynamic Shell Model Based on Intrinsic Differential Geometry

Abstract

The mathematical theory behind the modeling of shells is a crucial issue in many engineering problems. Here, the authors derive the free boundary conditions and associated strong form of a dynamic shallow Kirchhoff shell model based on the intrinsic geometry methods of Michael Delfour and Jean-Paul Zolésio. This model relies on the oriented distance function which describes the geometry. This is an extension of the work done in [J. Cagnol, I. Lasiecka, C. Lebiedzik and J.-P. Zolésio (2002). Uniform stability in structural acoustic models with flexible curved walls. J. Differential Equation, 186(1), 88–121.], where the model was derived for clamped boundary conditions only. In the current article, manipulations with the model result in a cleaner form where the displacement of the shell and shell boundary is written explicitly in terms of standard tangential operators.

Keywords:

• Shell
• Kirchhoff–Love
• Intrinsic modeling
• Free boundary conditions

Acknowledgment

Research was supported by the National Science Foundation under Grant INT-0104431.

Notes

^†E-mail: [email protected]

Additional information

Notes on contributors

Catherine Lebiedzik †

†E-mail: [email protected]