Planar problem of 3D-stability for a plate with crack (Q2754675)

A plane problem of stability of an isotropic thin elastic plate with a symmetric crack is considered. The direction of compressing force coincides with that of the crack. In the framework of the linearized elasticity theory, the problem is reduced to an eigenvalue problem for elastostatics equations in displacements under relevant boundary conditions at the plate boundary and the crack faces. For solution of the stability problem, it is sufficient to find the first eigenvalue. Approximate solution of the problem is found by numerical integration. A model example is considered and, a plot of critical load as a function of the crack length is presented. The critical load decreases when the crack length increases.