Numerical solution of differential and integral equations
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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