Transient analysis of a cracked functionally graded magneto‐electro‐elastic rectangular finite plane under anti‐plane mechanical and in‐plane electric and magnetic impacts

Abstract

The transient anti‐plane problem of a functionally graded magneto‐electro‐elastic (FGMEE) rectangular plane weakened by several embedded and edge cracks under various boundary conditions is solved. First, the solutions to the dynamic magneto‐electro‐elastic dislocation in the finite rectangular domain are derived by employing Laplace and finite Fourier cosine transforms. The solutions can be utilized to construct the singular integral equations in Laplace transform domain for FGMEE rectangular plane with multiple embedded and edge cracks. The integral equations arising from dislocation solutions have Cauchy‐type singularities with unknown dislocation density functions. These unknown functions may be obtained by reducing the integral equations into a system of linear algebraic equations, hereby, the dynamic stress intensity factors (DSIFs) for several arbitrarily embedded and edge cracks are obtained. The overshoots of dynamic stress intensity factors are shown to be intensely affected by the rectangular plane dimensions, length and position of the cracks, loading parameter, and negative or positive gradient index.