Reissner’s plate bending containing two not coaxial identical through-the-thickness cracks taking into account contact zone width of their faces [in Ukrainian].
Journal Title: Вісник Тернопільського національного технічного університету - Year 2015, Vol 80, Issue 4
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 crack 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 two parallel not shifted through-the-thickness equal cracks, 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, the vectors of which are parallel and perpendicular to the axes of the cracks. It is assumed that under external loading the cracks faces come in a smooth contact on all cracks length along the two-dimensional area of constant width near the upper plate basis. As a result of the cracks 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 using the Gauss method of reduction 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 cracks, force, bending moment, torque and transverse force intensity factors are constructed. In particular cases known in the scientific literature results for the Reissner’s plate bending problems with one crack considering the contact zone width of its faces, with two parallel cracks when their faces contact is considered only along the line 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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