Rocking forced displacement of a rigid disc embedded in a functionally graded transversely isotropic half-space

Abstract

Recent studies have confirmed that rockable structures have beneficial effects in earthquakes due to uniform dynamic behavior of the structure. For these kinds of structures, an equivalent static analysis is accurate enough, as the rocking motion is the dominant mode of their interaction with the surrounding soil (i.e. soil–structure interaction problem). In this study, the soil–structure interaction problems are extended to consider the effect of elastic non-homogeneities as well as changing the elasticity constants with depth in an exponential manner for the rocking loads. This paper analytically investigates the mixed boundary value problem regarding the forced rocking interaction of a rigid foundation embedded in a finite depth of an exponentially graded transversely isotropic half-space. The potential function method accompanied by Hankel integral transforms is applied to solve the system of the equations of motion of the media. Due to integral transforms used in the solving procedure, the mixed boundary value problem raised may be apt to be transformed to dual integral equations, which in turn, could be reduced to Fredholm integral equation of the second kind. To evaluate the solution of the integral equations, a robust numerical procedure has been developed for different anisotropic materials. Regarding the complicated integrand functions, the integrals are numerically and graphically presented to cover the effect of degree of change of material properties that plays a key role.

Three-dimensional dynamic Green’s functions in exponentially graded transversely isotropic tri-material composites

“…Selvadurai and Katebi [24] considered an incompressible elastic half-space with an exponential variation of the elastic shear modulus with depth, under acting of the axisymmetric interior load and they verified the accuracy of the corresponding solution via finite-element approach. Kalantari et al [25] analytically investigated the rocking behavior of a rigid disk, embedded in an exponentially graded transversely isotropic half-space. Then, they numerically presented the displacement and stress distribution as the solution to the Fredholm integral equation obtained.…”