1. Green's function for tangentialy loaded horizontaly layered half-spaceTomaž Pliberšek, Andrej Umek, 2008, original scientific article Abstract: The topic of this paper is a novel evaluation of the integral representation of the surface Greenćs function for a layered half-space, loaded on its surface by a harmonic tangential point force. The equations of motions are reduced to wave equations by the introduction of wave potentials. The Hankel transform is applied to them and they are consecutively solved leading to the integral representation of surface displacements. They are consecutively evaluated by the proposed three step procedure. First the singularity is extracted. It is further noted that so obtained integrals, after suitably chosen branch cuts and analytic continuation of integrands are introduced, can be evaluated by contour integration for an arbitrary number of layers. They are, therefore, expressed by number of residues at the poles of integrand and the integrals along finite portions of the branch cuts. The latter ones can easily be evaluated to any desired accuracy leading to a closed form solution. Some numerical results corroborating the presented approach are given.
Keywords: elastodynamics, elastic wave propagation, Green`s function, horizontaly layered half-space, horizontal point load
Published in DKUM: 05.06.2018; Views: 1407; Downloads: 88
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2. Green's function for an elastic layer loaded harmonically on its surfaceTomaž Pliberšek, Andrej Štrukelj, Andrej Umek, 2005, original scientific article Abstract: The Green's function in surface displacement plays an important role in soil structure interaction. In evaluating the Green's function, several difficulties occur because it is formulated in the infinite integral form. This paper outlines a method of analyzing the steady-state dynamic response of an elastic layer subjected to general point load excitation. It is assumed that the load is applied at the surface. The application Hankel integral transform, to the governing differential equations and boundary conditions yields the response displacements at the surface in integral representation. It will be shown that these semi-infinite integrals can be reduced to the integral with the finite range of integration, which can be efficiently taken numerically. The numerical results are presented, which show the efficiency of the developed procedure.
Keywords: civil engineering, geomechanics, soil-structure interaction, layered halfspace, Green's function, elastodynamics
Published in DKUM: 15.05.2018; Views: 1665; Downloads: 103
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3. Approximate expressions for the Green's functions of a semi-infinite, elastic mediumTomaž Pliberšek, Andrej Umek, 2010, original scientific article Abstract: On the basis of an exact, discretized presentation of the Green's function components, their closed-form approximations are developed. Their accuracy is considered to be better than the tolerances in the intrusive measurements data for the identification of the mechanical characteristics of soils. The use of these approximate expressions is believed to considerably reduce the computational effort in soil-structure interaction problems and open up new possibilities for the non-intrusive identification of soils.
Keywords: elastodynamics, half-space, Green's function, approximate solutions
Published in DKUM: 31.05.2012; Views: 2170; Downloads: 124
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