Contact Interaction of a Plate with a Nonlinear Elastic Stringer

A problem for determining the mechanical field in a homogeneous half-plane supported by a finite homogeneous stringer, material of which obeys the nonlinear Hooke law, is considered. The posed problem is reduced to a nonlinear singular integro-differential equation. Using the Schauder fixed-point th...

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Bibliographic Details
Published in:Mechanics of solids 2019-05, Vol.54 (3), p.440-447
Main Authors: Jokhadze, O. M., Kharibegashvili, S. S., Shavlakadze, N. N.
Format: Article
Language:English
Subjects:
Classical Mechanics
Differential equations
Existence theorems
Fixed points (mathematics)
Physics
Physics and Astronomy
Schauder fixpoint theorem
Singular integral equations
Stringers
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Summary:A problem for determining the mechanical field in a homogeneous half-plane supported by a finite homogeneous stringer, material of which obeys the nonlinear Hooke law, is considered. The posed problem is reduced to a nonlinear singular integro-differential equation. Using the Schauder fixed-point theorem, the existence of a solution for this equation is proved. Using the small parameter method, a system of recurrence linear singular integral equations of the first kind is obtained.
ISSN:0025-6544
1934-7936
DOI:10.3103/S0025654419020080