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Non-classical problems of fluid-elastic cusped plate (beam) interaction (1-3339-TB-06)


Funded by

Georgian Civilian Research and Development Foundation/U.S. Civilian Research and Development Foundation

Start Date: 2007-05-01       End Date: 2009-04-30

Boundary value problems in the general -th approximation for hierarchical models of cusped prismatic shells, which as three-dimensional bodies have non-Lipschitz boundaries, in the cases, when at least on a part of the prismatic shell projection boundary displacements are prescribed, are investigated.
It is well-known that by means of the present state of mathematical methods it is not possible to study elastic bodies with non-Lipschitz boundaries. By the investigation carried out for such bodies in the -th hierarchical model this gap is filled in some sense.
The fluid-solid interaction problems are investigated in the case of Lipschitz and non-Lipschitz domains, when in the fluid part the linearized Navier-Stokes equations are considered, while in the solid part either equations of three-dimensional linear elasticity, or hierarchical models of prismatic shells, or initial hierarchical models of cusped prismatic beams are used.
Some problems for cusped plates with transverse shear deformations (Reisner-Mindlin type model) and their interaction with viscous fluid is studied; a special flexible cusped beams on the base of the classical non-linear bending theory is treated.

Project members:

Talks

  • Elastic Cusped Beam, Plate, and Shell Models and Their Relation to Three-dimensional Linear Models, by George Jaiani (Speaker) at Analysis and PDE Seminar (guided by Prof. R.P. Gilbert), 2007, Delaware, USA.

Publications

  • Natalia Chinchaladze, Robert Gilbert, George Jaiani, Sergo Kharibegashvili, David Natroshvili, Existence and Uniqueness Theorems for Cusped Prismatic Shells in the N-th Hierarchical Model, Mathematical Methods in Applied Sciences, Vol. 31, No. 11, 1345-1367, Wiley, 2008.
  • Natalia Chinchaladze, Robert Gilbert, George Jaiani, Sergo Kharibegashvili, David Natroshvili, Cusped Elastic Beams under the Action of Stresses and Concentrated Forces, Applicable Analysis, Volume 89, No. 5, 757–774, Taylor and Francis Ltd., 2010.
  • Natalia Chinchaladze, Robert Gilbert, George Jaiani, Sergo Kharibegashvili, David Natroshvili, Initial-boundary value problems for solid–fluid composite structures, Zeitschrift für angewandte Mathematik und Physik volume 63, pages625–653, Springer, 2012.