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With the aid of a complete representation using two displacement potentials, an efficient and accurate analytical derivation of the fundamental Green's functions for a transversely isotropic elastic half-space subjected to an arbitrary, time-harmonic, finite, buried source is presented. The formulation includes a complete set of transformed stress-potential and displacement-potential relations that can be useful in a variety of elastodynamic as well as elastostatic problems. The present solutions are analytically in exact agreement with the existing solutions for a half-space with isotropic material properties. For the numerical evaluation of the inversion integrals, a quadrature scheme... 

By virtue of a method of displacement potentials, an analytical treatment of the response of a transversely isotropic substrate-coating system subjected to axisymmetric time-harmonic excitations is presented. In determination of the corresponding elastic fields, infinite line integrals with singular complex kernels are encountered. Branch points, cuts, and poles along the path of integration are accounted for exactly, and the physical phenomena pertinent to wave propagation in the medium are also highlighted. For evaluation of the integrals at the singular points, an accurate analytical residual theory is presented. Comparisons with the existing numerical solutions for a two-layered... 

An analytical approach has been applied to obtain the solution of Navier's equation for a homogeneous, isotropic half-space under an inertial foundation subjected to a timeharmonic loading. Displacement potentials were used to change the Navier's equation to a system of wave-type equations. Calculus of variation was employed to demonstrate the contribution of the foundation's inertial effects as boundary conditions. Use of the Fourier transformation method for the system of Poisson-type equations and applying the boundary conditions yielded the transformed surface displacement field. Direct contour integration has been employed to achieve the surface waves. In order to clarify the... 

An analytical derivation of the elastodynamic fundamental solutions for a transversely isotropic tri-material full-space is presented by means of a complete representation using two displacement potentials. The complete set of three-dimensional point-load, patch-load, and ring-load Green's functions for stresses and displacements are given, for the first time, in the complex-plane line-integral representations. The formulation includes a complete set of transformed stress-potential and displacement-potential relations in the framework of Fourier expansions and Hankel integral transforms, that is useful in a variety of elastodynamic as well as elastostatic problems. For the numerical... 

With the aid of a method of displacement potentials, an efficient and accurate analytical derivation of the three-dimensional dynamic Green's functions for a transversely isotropic multilayered half-space is presented. Constituted by proper algebraic factorizations, a set of generalized transmission-reflection matrices and internal source fields that are free of any numerically unstable exponential terms are proposed for effective computations of the potential solution. Three-dimensional point-load Green's functions for stresses and displacements are given, for the first time, in the complex-plane line-integral representations. The present formulations and solutions are analytically in exact... 

Two new displacement potential functions are introduced for the general solution of a three-dimensional piezoelasticity problem for functionally graded transversely isotropic piezoelectric solids. The material properties vary continuously along the axis of symmetry of the medium. The four coupled equilibrium equations in terms of displacements and electric potential are reduced to two decoupled sixth- and second-order linear partial differential equations for the potential functions. The obtained results are verified with two limiting cases: (i) a functionally graded transversely isotropic medium, and (ii) a homogeneous transversely isotropic piezoelectric solid. The simplified relations... 

This study deals with the elastodynamic response of a surface-stiffened transversely isotropic half-space subjected to a buried time-harmonic normal load. The half-space is reinforced by a Kirchhoff thin plate on its surface. By virtue of a displacement potential function and appropriate time-harmonic Green’s functions of transversely isotropic half-spaces, a robust solution corresponding to two plate-medium bonding assumptions, namely (a) frictionless interface, and (b) perfectly bonded interface is obtained for the first time. All elastic fields of the problem are expressed explicitly in the form of semi-infinite line integrals. Results of some limiting cases including isotropic materials,... 

The stress fields of cylindrical and spherical multi-phase inhomogeneity systems with perfect or imperfect interfaces under uniform thermal and far-field mechanical loading conditions are investigated by use of the Boussinesq displacement potentials. The radius of the core inhomogeneity and the thickness of its surrounding coatings are arbitrary. The discontinuities in the tangential and normal components of the displacement at the imperfect interfaces are assumed to be proportional to the associated tractions. In this work, for the problems where the phases of the inhomogeneity system are homogeneous, the exact closed-form thermo-elastic solutions are presented. These solutions along with a... 

The analytical treatment of an axisymmetric rigid punch indentation of an isotropic half-space reinforced by a buried extensible thin film is addressed. With the aid of appropriate displacement potential functions, Hankel transforms, and some mathematical techniques, the mixed boundary value problem under consideration is reduced to a Fredholm integral equation of the second kind. The most interesting results of the problem, including the equivalent normal stiffness of the system and the contact stress distribution beneath the rigid punch, are expressed in terms of the solution of the obtained Fredholm integral equation. Some limiting cases corresponding to inextensible and extremely... 

Green's functions of a transversely isotropic half-space overlaid by a thin coating layer are analytically obtained. The surface coating is modeled by a Kirchhoff thin plate perfectly bonded to the half-space. With the aid of superposition technique and employing appropriate displacement potential functions, the Green's functions are expressed in two parts; (i) a closed-form part corresponding to the transversely isotropic half-space with surface kinematic constraints, and (ii) a numerically evaluated part reflecting the interaction between the half-space and the plate in the form of semi-infinite integrals. Some limiting cases of the problem such as surface-stiffened isotropic half-space,... 

By virtue of a complete set of displacement potential functions and Hankel transform, the analytical expressions of Green's function of an exponentially graded elastic transversely isotropic half-space is presented. The given solution is analytically in exact agreement with the existing solution for a homogeneous transversely isotropic half-space. Employing a robust asymptotic decomposition technique, the Green's function is decomposed to the closed-form Green's function corresponding to the homogeneous transversely isotropic half-space and grading term with strong decaying integrands. This representation is very useful for numerical methods which are based on boundary-integral formulations...