# Институт вычислительной математики

и математической геофизики

# The International Conference on Computational Mathematics

ICCM-2004

June, 21-25, 2004
Novosibirsk, Academgorodok

## Abstracts

*Numerical solution of differential and integral equations*

## Statement and numerical investigation of stationary problems on contact of a soft shells and a barrier

**Kazan State University Kremlevckaja st.,**

18 (Kazan)

We consider the plane and spatial problems on determination of the equilibrium state of a soft shells fixed on edges, being under action of mass and surface loads, and restricted in its motion by a barrier. Finite deformations and increments of the shells are admitted. We study the problems on equilibrium state of a soft shell under the condition that the surface of the barrier is described by a sufficiently smooth (not necessarily convex) function. First, starting from the equilibrium equations written in the Cartesian coordinate system, we formulate a pointwise problems. Afterwards, on the basis of the principle of virtual displacements, we obtain its variational formulations. Then we consider the case of a soft netlike shell formed by two families of threads. Under certain conditions upon the functions describing physical relations in the threads, we state a generalized problems in the form of a quasivariational inequalities in a Banach space and establish its solvability. For solving of considering problemes the iterative methods are suggested. In the plane case their convergence is investigated. The numerical experiments are carried out.

*Note. Abstracts are published in author's edition*

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Last update: 06-Jul-2012 (11:52:06)