Based on complex function theory, an analytical solution for the dynamic stress concentration due to an arbitrary cylindrical cavity in an infinite inhomogeneous medium is investigated. Two different conformal mappings are introduced to solve scattering by an arbitrary cavity for the Helmholtz equation with variable coefficient through the transformed standard Helmholtz equation with a circular cavity. By assuming that the medium density continuously varies in the horizontal direction with an exponential law and the elastic modulus is constant, the complex-value displacements and stresses of the inhomogeneous medium are explicitly obtained. The distribution of the dynamic stress for the case of an elliptical cavity are obtained and discussed in detail via a numerical example. The results show that the wavenumber, inhomogeneous parameters, and different values of aspect ratio have a significant influence on the dynamic stress concentration factors around the elliptical cavity.

Frost resistance is a very important durability criterion of concrete in the cold environment. To improve the frost resistance of concrete, carbon fiber was added into the concrete. Repeated soaking in water will accelerate the freeze-thaw damage of concrete, resulting in mass loss and the compressive strength decrease of the concrete. Thus, a recurrent freeze-thaw experiment, in which specimens of carbon-fiber-reinforced concrete were frozen for 4 h and then thawed in the warm water for 4h, was carried out to estimate the relationship of the addition of carbon fiber and frost resistance. The results show that adding the carbon fiber into concrete could reduce the mass loss of the concrete during the freeze-thaw experiment. And when the carbon fiber content is more than 0.50 wt.‰, the increase in the carbon fiber content improved the compressive strength of the concrete significantly. The frost-resistance of the plain concrete is 100 freeze–thaw cycles, after which the compressive strength losses were 21.2% and 9.0%, respectively. When the optimal adding amount of carbon is 1.5 wt.%, the frost-resistance of the concrete is 250 cycles. It indicates that the carbon-fiber-reinforced concrete is suitable for buildings in cold and moist conditions.