On the buckling of the elastic and viscoelastic composite circular thick plate with a penny-shaped crack

Buckling problem of the elastic and viscoelastic rotationally symmetric thick circular plate with a penny-shaped crack is investigated. It is supposed that the crack edges have a small initial rotationally symmetric imperfection. The lateral boundary of the plate is clamped and the clamp compresses this plate circumferentially and inwards by a fixed radial displacement. The investigations are carried out in the framework of the exact geometrically non-linear equations of the theory of viscoelasticity and as a buckling criterion the case for which the initial imperfection of the crack edges start to increase indefinitely is taken. Numerical results are obtained using the Laplace transform and finite element method and are compared with the known ones for elastic composites.