A Complete Solution of the Wave Equations for Transversely Isotropic Media

SUMMARYA boundary integral equation method is presented for a rigid cylindrical pipe-pile of finite length embedded in a transversely isotropic half-space under lateral loads. In the framework of three-dimensional elastostatics, the complicated soil-structure interaction problem is shown to be reducible to three coupled Fredholm integral equations. Through an analysis of the associated Cauchy singular kernels, the intrinsic singular characteristics of the radial, angular, and vertical interfacial load transfers are rendered explicit. By means of a complicated numerical procedure, detailed results on the three-dimensional load-transfer process are provided for benchmark comparison and practical applications.

Section: Green's Functions For Three-dimensional Half-spacementioning

confidence: 99%

Rigid cylinder in a transversely isotropic half‐space under lateral loads

Shahmohamadi

Khojasteh

Rahimian

et al. 2011

“…In order to uncouple Equation (9) a potential functions F introduced by Eskandari-Ghadi [22] is used. This potential function, F, is related to displacement components, u r and u z as…”

Section: Statement Of the Problem And The Governing Equationmentioning

confidence: 99%

Axisymmetric interaction of a rigid disc with a transversely isotropic half‐space

Katebi

Khojasteh

Rahimian

et al. 2010

SUMMARYA theoretical formulation is presented for the determination of the interaction of a vertically loaded disc embedded in a transversely isotropic half-space. By means of a complete representation using a displacement potential, it is shown that the governing equations of motion for this class of problems can be uncoupled into a fourth-order partial differential equation. With the aid of Hankel transforms, a relaxed treatment of the mixed-boundary value problem is formulated as dual integral equations, which, in turn, are reduced to a Fredholm equation of the second kind. In addition to furnishing a unified view of existing solutions for zero and infinite embedments, the present treatment reveals a severe boundary-layer phenomenon, which is apt to be of interest to this class of problems in general. The present solutions are analytically in exact agreement with the existing solutions for a half-space with isotropic material properties. To confirm the accuracy of the numerical evaluation of the integrals involved, numerical results are included for cases of different degrees of the material anisotropy and compared with existing solutions. Further numerical examples are also presented to elucidate the influence of the degree of the material anisotropy on the response.

“…Wang and Wang [24] proved the completeness of the elastostatic solutions called Lekhnitskii-Hu-Nowacki solution [25] and Elliott [26] function. Eskandari-Ghadi [27] introduced a complete set of scalar potential functions for the elastodynamic problems related to transversely isotropic axially convex domain, which have been utilized to investigate the wave propagation and singularities in this study. Recently, Rahimian et al [28] solved the dual integral equations due to forced torsion vibration of a rigid circular disc attached on the surface of a transversely isotropic half-space, and Katebi et al [29] have made an in-depth investigation for the analytical solution of an axially symmetric interaction of a rigid disc with a transversely isotropic half-space in the static case.…”

Section: Introductionmentioning

confidence: 99%

“…The coupled partial differential equations are uncoupled with the use of potential functions introduced in [27]. Utilizing the Fourier series and the Hankel integral transforms [30], the relaxed treatment of mixed boundary-value problem formulated in this paper is transformed into two pairs of integral equations, called dual integral equations.…”

Section: Introductionmentioning

confidence: 99%

Rocking vibration of a rigid circular disc in a transversely isotropic full‐space

Eskandari‐Ghadi

Mirzapour

Ardeshir-Behrestaghi

2010

Self Cite

SUMMARYIn this paper, forced rocking vibration of a rigid circular disc placed in a transversely isotropic full-space, where the axis of material symmetry of the full-space is normal to the surface of the plate, is analytically investigated. Because of using the Fourier series and Hankel integral transforms, the mixed boundary-value problem is transformed into two separate pairs of integral equations called dual integral equations. The dual integral equations involved in this paper are reduced to Fredholm integral equations of the second kind. With the aid of contour integration, the governing integral equation is numerically evaluated in the general dynamic case. The reduced static case of the dual integral equations is solved analytically and the vertical displacement, the contact pressure and the static impedance/compliance function are explicitly determined, and it is shown that the pressure in between the plate and the full-space and the compliance function reduced for isotropic half-space are identical to the previously published solutions. The dynamic contact pressure in between the disc and the space and also the related impedance function are numerically evaluated in general dynamic case and illustrated. It is shown that the singularity exists in the contact pressure at the edge of the disc is the same as the static case. To show the effect of material anisotropy, the numerical evaluations are given for some different transversely isotropic materials and compared.