Dynamic stress analysis of elliptical inclusions in an inhomogeneous medium with modulus and density variations under the action of shear horizontal (SH) waves

Abstract

In this paper, in connection with the problem of elastic wave propagation in a continuously inhomogeneous medium, the dynamic stress concentration phenomenon caused by the elliptical inclusions in a complex, continuously inhomogeneous medium under the action of shear horizontal (SH) waves is studied. First, the auxiliary function and the shear modulus function are introduced to construct the wave field function, and the modulus is reduced in order and simplified using a high-order fluctuating wave equation with variable coefficients that has power function variations; then, the auxiliary function and the modulus function are introduced once again to construct the density function; finally, the conformal mapping method is used to carry out coordinate transformation and to solve and obtain the standard form of the Helmholtz equation. Based on this combined problem model, the wave field and the stress field are derived, and the expression for the dynamic stress concentration factor (DSCF) is given. The influence of the inhomogeneous parameters, the ratio of the long and short axes of the elliptical inclusions, and the relative properties of the elliptical inclusions and the matrix on the DSCF around the elliptical inclusions is analyzed through calculation examples.