Stress Concentration of Lining Structure in Unbounded Inhomogeneous Medium Subjected to SH Waves

The stress concentration around the lining structure in unbounded inhomogeneous media under SH waves is solved according to complex theory. In this work, the shear modulus is the function of spatial coordinates and density is assumed to be a constant. By introducing complex variables, the governing equations in complex coordinate system in heterogeneous media are given, and the governing equations in heterogeneous media are obtained. The wave field expressions which strictly satisfy the governing equations and boundary conditions are gained. The coefficients that are not determined can be acquired according to boundary conditions. In the situation of selecting appropriate parameters, the results of this work are compared with the published results, the method of this work can be verified. The influences of lining thickness and inhomogeneous parameters on stress concentration are analyzed by numerical examples, the difference between inner boundary and outer boundary of lining structure is discussed.