Nonstationary random vibration analysis of cracked plates by SFBEM-FEM coupling method

Dynamic reliability analysis of crack problems is of great concern to engineering practice. To tackle this problem, dynamic stress intensity factors (SIFs) of cracks need to be computed at high accuracy and efficiency with wide adaptability. In this study, a cracked superelement is first proposed to model the near-crack region. The stiffness matrix and mass matrix of the cracked superelement are formulated by the dynamic spline fictitious boundary element method (SFBEM) based on the Erdogan fundamental solutions. The proposed superelement is then incorporated into a finite element mesh, and the global equation of motion of the crack problem is established and solved within the frame of finite element method (FEM). The explicit time-domain expressions of dynamic SIFs of the crack problem are finally constructed by a backward analysis of the cracked superelement with SFBEM. On this basis, the explicit time-domain method (ETDM) is utilized to conduct random vibration analysis of the crack problem subjected to nonstationary random loads. The statistical moments of dynamic SIFs and the failure probability of initial crack propagation can be evaluated at high efficiency by ETDM in conjunction with the SFBEM-FEM coupling method. Numerical examples are investigated to show the effectiveness of the proposed hybrid approach.