Bending of isotropic plate with square washer and stiff straight crack taking into account crack sides contact area width
Journal Title: Вісник Тернопільського національного технічного університету - Year 2015, Vol 78, Issue 2
Abstract
As a widely used industry lamellar structural elements, the strength of which are highly dependent on the type of defects cracks dramatically reduce the carrying capacity and operation design. As you know, these crack-like defects can occur both during the production design, and during its operation. Therefore the main task in assessing the allowable load of defect structures are effort and intensity factors moments. In this paper we solve the problem of bending of isotropic plates with tight square washer and crack based on the width contact area, where it was placed on the axis of symmetry inclusion. Through contact crack solution to the problem is presented in the form of two problems: the plane problem of elasticity and bending problem, where we use the classical theory of bending plates. We will have boundary conditions on the boundary rigid inclusion and crack. To construct the solution of the plane problem and bending problem, we introduce the complex potentials as a sum of complex potentials for inclusion and crack. Based on the known dependencies that determine the stress-strain state of the plate potentials through the complex potentials after satisfaction of the boundary conditions for cracks and for inclusion singular integral equations have been obtained. This condition should correspond uniqueness deflection and rotation angles while traversing path cracks and unambiguous movements while traversing path cracks. After bringing the unknown functions and variables to dimensionless final system of singular integral equations with unknown complex functions and constants have been obtained. The resulting system of singular integral equations by the method of mechanical quadratures was reduced to a system of linear algebraic equations. This system of equations by Gauss with a choice of main element was numerically solved, and on the basis of these data were analyzed. The numerical analysis of the contact force between the shores of crack intensity factors moments of critical load for different values of parameters of the problem has been carried out. Based on numerical analysis, the following laws were stated: the value of the contact force is larger near the top than in the distant, and at a distance from the split washers, contact forces and combined intensity factor moments go to the constant value for a single crack.
Authors and Affiliations
Victor Opanasovich, Mykola Slobodyan, Vasyl Bedriy
Keywords
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