Reissner’s plate bilateral bending containing coaxial through-the-thickness slit and crack taking into account contact zone width of its faces
Journal Title: Вісник Тернопільського національного технічного університету - Year 2015, Vol 79, Issue 3
Abstract
Construction of the cracked plate bending problems solutions forms an important and actual in terms of theory development and practical applications scientific direction. They make it possible to determine stress and displacement distribution near the defects tips, as well as make recommendations for selecting optimal geometrical, physical and mechanical characteristics of plates depending on operating conditions in order to prevent destruction of engineering constructions. In this paper the stress-strain state of boundless isotropic plate with coaxial through-the-thickness slit and crack, the faces of which are free from the external loading is investigated. The plate is under the action of the uniformly distributed in a remote part bending moments, which vectors are parallel and perpendicular to the axe of the defects. It is assumed that under external loading the crack faces come in a smooth contact on all crack length along the two-dimensional area of constant width near the upper plate basis. As a result of the crack faces contact the solution of problem is presented in the form of two related problems solutions: the theory of elasticity plane problem and the problem of plates bending based on the equations of Reissner theory. On the basis of complex variable function theory methods and complex potentials the system of singular integral equations is obtained which is reduced by the mechanical quadratures method to the infinite system of linear algebraic equations. This system is solved numerically by the method of reduction using Gauss with a choice of main entry. The numerical analysis of problem at some parameters values is carried out and graphic dependences for contact force between the faces of crack, force and moment intensity factors are constructed. In particular cases known in the scientific literature results for Reissner’s plate bending problems with one crack considering the contact zone width of its faces, with two coaxial slits as well as for appropriate problems solved using equations of the classical theory of plates bending are obtained.
Authors and Affiliations
Heorhiy Sulym, Viktor Opanasovych, Ihor Yatsyk
Keywords
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