Dynamic Stress Analysis Around a Circular Cavity in Two-Dimensional Inhomogeneous Medium with Density Variation

Abstract

AbstractBased on the complex function theory and the homogenization principle, an universal approach of solving the dynamic stress concentration around a circular cavity in two-dimensional (2D) inhomogeneous medium is developed. The Helmholtz equation with variable coefficient is converted to the standard Helmholtz equation by means of the general conformal transformation method (GCTM) analytically. As an example, the inhomogeneous medium with density varying as a function of two spatial coordinates and the constant elastic modulus is studied. The dynamic stress concentration factors (DSCF) are calculated numerically. It shows that medium inhomogeneous parameters and wave numbers have significant influence on the dynamic stress concentration by the circular cavity in two-dimensional inhomogeneous medium.