The existence of solutions is proved for the unilateral dynamic contact of a von Kármán-Donnell shell with a rigid obstacle. Both purely elastic material and a material with a singular memory are treated.

Abstract– This article describes an investigation into the free vibration of double-walled carbon nanotubes (DWCNTs) using a nonlocal elastic shell model. Eringen’s nonlocal elasticity is implemented to incorporate the scale effect into the Donnell shell model. Also, the van der Waals interaction between the inner and outer nanotubes is taken into account. A new numerical solution method from i...

iii ACKNOWLEDGEMENTS I wish to thank Dr. Komerath, my research advisor. It has been a true honor, to work with him in his research endeavors. In addition to the great opportunity he has given me, he has always listened to my ideas, and given me his confidence, respect, encouragement, and support. I am forever indebted. I would like to thank my mother and father for everything. I would like than...

Recent results concerning the application of Lie transformation group methods to structural mechanics are presented. Focus is placed on the point Lie symmetries and conservation laws inherent to the Bernoulli–Euler and Timoshenko beam theories as well as to the Marguerrevon Kármán equations describing the large deflection of thin elastic shallow shells within the framework of the nonlinear Donn...

M Arnold--Chamney, S Bateman, K Owen, Jesudason, McDonald, O Pearson, N Sinclair, I Williamson, O, Donnell K, J Kelly

We deal with an initial-boundary value problem describing the perpendicular vibrations of a viscoelastic Kármán-Donnell shell with a rigid inner obstacle. A weak formulation of a problem is in a form of a hyperbolic variational inequality. We solve this problem using the penalization method

Drew Michael S. Donnell, Jessica L. Seidelman, Christopher L. Mendias, Bruce S. Miller, James E. Carpenter and Richard E. Hughes* Department of Orthopaedic Surgery, University of Michigan, 2017 Biomedical Research Building, 109 Zina Pitcher Place, Ann Arbor, MI, USA; Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI, USA; Department of Industrial & Operations Engineeri...

We deal with initial-boundary value problems describing vertical vibrations of viscoelastic von Kármán-Donnell shells with a rigid inner obstacle. The short memory (Kelvin-Voigt) material is considered. A weak formulation of the problem is in the form of the hyperbolic variational inequality. We solve the problem using the penalization method.