An extended finite element framework for vibration analysis of cracked FGM shells

Given the widespread use of FGM shell elements in numerous industrial fields and their extreme vulnerability to crack formation, the present work is directed towards investigating the vibrational behavior of cracked FGM shells. A general XFEM formulation, with tested accuracy and performance, is presented due to its intrinsic capability to handle problems with discontinuities, such as cracks. To demonstrate the performance of the adopted approach, multiple examples are introduced and analyzed and the effects of various parameters such as the length and angle of the crack and different distribution patterns of material stiffness and density across the thickness of the shell, are extensively studied. Five cracked FGM models, including a rectangular plate, a circular plate with four radial cracks, a cylindrical shell, a conical shell and a spherical dome are simulated by the proposed approach and the results are discussed.