Dynamic stress analysis of functionally gradient material subject to SH waves

In this paper, the wave propagation in functionally graded materials (FGM) is studied by the elastic wave theory based on the wave problems in homogeneous media. The auxiliary function and modulus function are introduced to construct the displacement field and density function. The displacement field, modulus function, and density function are connected to propose a design theory of special FGM. An analytical method for elastic wave propagation in inhomogeneous media with varying modulus and density is derived to provide theoretical references for material design and dynamic stress analysis under elastic waves. Taking the problem of dynamic stress concentration caused by shallow buried elliptical cavity in half space designed under SH waves as an example, the calculation results are obtained and analyzed. The results show that the dynamic stress concentration is sensitive to the change of the inhomogeneity of the medium.