Keywords: rectangular inner-crack, buckling delamination, critical force, thick rectangular plate, composite material, finite element method.

In this study, the buckling delamination problem for the rectangular composite plate with a rectangular inner crack is investigated. It is assumed that all the edge surfaces of the plate considered are simply supported, i.e. the edge surfaces' displacements can not move along the Ox₂ axis. In the initial state we assume that the edge-surfaces of the crack has an initial infinitesimal imperfection. The evolution of this initial imperfection with an external compressive loading acting on the plate ends is studied by the use of the three-dimensional geometrically non-linear field equations of the theory of elasticity for anisotropic bodies. The solution of the nonlinear boundary value problem considered is presented in the series form using a parameter which characterizes the degree of the crack surfaces' initial imperfections. As a result of a cumbersome mathematical procedure the investigation of this non-linear boundary value problem is reduced to the investigation of a series of linear boundary value problems.

The investigations carried out in [1,2,3] indicate that the values of the critical force can be determined only within the framework of the zeroth and the first approximations. The second and the subsequent approximations do not change the values of the critical forces. Taking these subsequent approximations into account improves only the accuracy of the distributions of stresses in the plate. Since our aim is to investigate the values of the critical buckling forces as well as the buckling delamination mode, we restrict ourselves to the zeroth and the first approximations.

The considered boundary value problems formulated for the zeroth and the first approximations are solved with employing a three-dimensional finite element method. All algorithms and programs used by obtaining the numerical results have been composed by the authors in the FTN77. Concrete numerical results are attained for the case where the material of the plate considered is a homogeneous, transversally isotropic one. The influence of geometrical and material parameters on the critical forces and buckling modes are analyzed and discussed. In particular, it is established that the buckling form depends not only on the initial infinitesimal imperfection mode of the crack edges, but also on the ratio of the rectangular crack lengths along the Ox₁ and Ox₃ axes.

1

S.D. Akbarov, O.G. Rzayev, "On the Buckling of the Elastic and Viscoelastic Composite Circular Thick Plate with a Penny-Shaped Crack", European Journal of Mechanics A/Solids, 21(2), 269-279, 2002. doi:10.1016/S0997-7538(01)01196-2

2

O.G. Rzayev, S.D. Akbarov, "Local Buckling of the Elastic and Viscoelastic Coating Around the Penny-Shaped Interface Crack", International Journal of Engineering Science, 40, 1435-1451, 2002. doi:10.1016/S0020-7225(02)00034-4

3

S.D. Akbarov, N. Yahnioglu, E.E. Karatas, "Buckling Delamination of the Viscoelastik Rectangular Thick Plate with an Edge Rectangular Crack", ASME 2009 International Mechanical Engineering Congress and Exposition (IMECE09), Lake Buena Vista, Florida, USA, 2009.

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