Compressive buckling of laminates with an embedded delamination

In this paper, a buckling analysis of laminates with an embedded delamination has been conducted by employing a finite-element method based on the Mindlin plate theory. An effective solution method has been put forward to deal with the contact problem in the buckling mode. In this method, an iterative updating process incorporating first-order sensitivity analysis and quadratic programming technique has been proposed for computing fictitious forces in the contact area, which can be used to calculate stiffness parameters of some artificial springs. Finally, the penetration between two delaminated layers in the buckling mode can be effectively prevented by inserting these artificial springs into the overlapped area in the buckling mode. Numerical examples indicated that this method is very efficient for solving the contact problem in buckling analysis. Its accuracy and convergence speed are very high. The numerical results demonstrate that the contact analysis is very important for buckling analysis in some cases. The effects of various sizes, shapes and positions of the delamination and the fiber angle of the sublaminate on the buckling load have also been investigated.