Anti‐plane stress analysis for V‐notch in a piezomagnetic half space under SH wave

Abstract

In this paper, the anti‐plane stress analysis of a V‐notch with complex boundary conditions in a piezomagnetic half space is studied. Firstly, SH wave is considered as an external load acting on piezomagnetic half space, on the basis of repeated image superposition, the analytical expression of scattering wave is conducted, which satisfies the boundary conditions on the boundary of the half space. Then, the analytical expression of standing wave is established, which satisfies the stress free and magnetic insulation conditions on the boundaries of V‐notch by the fractional Bessel function expansion method and Graf addition theorem. Finally, Green's function method is applied, the half space is divided into two parts along the vertical interface, a pair of in‐plane magnetic field and out‐plane forces are applied on the vertical interface, and the first kind of Fredholm integral equations are set up and solved by applying orthogonal function expansion technique and effective truncation. Results clarified the influence on the dynamic stress concentration factor and magnetic field intensity concentration factor under proper conditions. Besides, the analytical solutions are compared with the finite element solutions to verify the accuracy of the conclusions in this article.