Analytical and numerical solution of the stress field and the dynamic stress intensity factors in a cracked plate under sinusoidal loading

A cracked plate subjected to a sinusoidal loading perpendicular to its plane is considered, and the analytical solution of the dynamic vibration behavior of a plate, which allowed the determination of the stress field near the crack tip, is developed. A mixed mode of loading near the crack tip has been established and described with dynamic stress intensity factors K I (z,t) and K II (z,) associated with modes I and II crack openings, respectively. To validate the analytical results, a finite element analysis (FEA) of a 1 × 1 m square plate with a thickness of 1 cm, having a middle crack of 10 cm in length, is made. The results have shown significant agreement between analytical and FEA findings. © ASM International 2008.