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Combined bending with tension of isotropic plate with crack considering crack banks contact and plastic zones at its tops

100%

Sulym H. , Opanasovych V. , Slobodian M. , Bilash O.

Acta Mechanica et Automatica

2018

tom Vol. 12, no. 2

91--95

Stress-strain state of isotropic plate with rectilinear through-crack at combined action of bending and tension, realized by applying distributed forces and bending moments at infinity, the vectors of which are parallel and perpendicular to the crack, is investigated. Under the influence of the internal stress the crack faces contacts on area of constant width near the upper base of plate, and plastic zones forms in its tips. Using methods of the theory of complex variables, complex potentials plane problem of elasticity theory and the classical theory of plates bending, solving of the problem is reduced to the set of linear conjugation problems and their analytical solution is built in a class of functions of limited plastic zones in the crack tips. The conditions of existence of the solution of the problem in these terms are determined. Using Treska plasticity conditions in the form of surface layer or the plastic hinge, the length of plastic zone and crack opening displacement are found analytically. Their numerical analysis for various parameters of the problem is conducted.

Influence of asymptotic corrector on the description of the dynamic behaviour of a circular elastic plate

58%

Sławianowska A. , Telega J. J.

tom Vol. 56, nr 1

19-31

The aim of the present paper is to study an initial-boundary value problem for an isotropic circular plate. General theory was developed by the authors in [12]. The novelty consists in the study of influence of second-order terms (correctors), obtained by variational-asymptotic analysis, on the dynamic solution of plates.