Nonclassical biharmonic boundary value problems describing bending of finite and infinite plates with inclusions
type: Item
instance of: scholarly article
zbMATH Open document ID: 1005.74038
publication date: 2003-02-05T00:00:00Z
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74M15
Mathematics Subject Classification ID: 45B05
zbMATH DE Number: 1625284
zbMATH Keywords: contact problems
zbMATH Keywords: plate bending
zbMATH Keywords: elasticity theory
zbMATH Keywords: circular plate
zbMATH Keywords: rectangular plate
zbMATH Keywords: characteristic equation
zbMATH Keywords: Prandtl integro-differential equation
zbMATH Keywords: singular operator
zbMATH Keywords: Fredholm integral equations of second kind
zbMATH Keywords: contact stresses
zbMATH Keywords: anisotropic plates
MaRDI profile type: Publication
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author: N. Shavlakadze
title: Nonclassical biharmonic boundary value problems describing bending of finite and infinite plates with inclusions
published in: Memoirs on Differential Equations and Mathematical Physics
review text: The author studies contact problems of elasticity theory related to the bending of finite and infinite, isotropic or anisotropic plates with an elastic inclusion of variable rigidity. The circular plate and rectangular plate are considered as particular cases. The problems are reduced to integro-differential equations with variable coefficient. The characteristic equation corresponding to these equations is Prandtl integro-differential equation when the coefficient of singular operator possesses zeros of higher order at the end points of the interval of integration. First, the author investigates the properties of the solution of characteristic equation. Then the integro-differential equations are reduced to Fredholm integral equations of the second kind. The author obtains exact and approximate solutions, and examines the behaviour of contact stresses at the ends of contact line. The corresponding problems for anisotropic plates are discussed at the end.
reviewed by: Nikolai Pleshchinskii
description: scientific article; zbMATH DE number 1625284