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.