Two dimensional transient fundamental solution due to suddenly applied load in a half-space

Guan, Fenhai; Moore, Ian D.; Spyrakos, Constantine C.

doi:10.1016/s0267-7261(97)00037-7

Cited by 16 publications

(12 citation statements)

References 11 publications

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“…This path was followed for the homogeneous case, i.e., a = 0 and with F(t) = 1, in [Guan et al 1998]. …”

Section: Time-harmonic Elastodynamic Green's Function For the Half-plmentioning

confidence: 99%

“…thesis, quoted in [Kobayashi 1983]. A corresponding Green's function in the Laplace domain for a homogeneous half-plane can be found in [Guan et al 1998], while an approximate such function using an image source across the free surface was derived earlier in [Kontoni et al 1987]. Finally, the transient Green's function due to a suddenly applied load in the homogeneous half-plane, namely Lamb's problem, can be found in [Kausel 2006], a compilation of fundamental solutions in elastodynamics.…”

Section: Introduction and Problem Statementmentioning

confidence: 99%

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Time-harmonic elastodynamic Green’s function for the half-plane modeled by a restricted inhomogeneity of quadratic type

Rangelov

Manolis

2010

J. Mech. Mater. Struct.

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We derive closed-form solutions for point-force generated motions in a continuously inhomogeneous half-plane, which represent the complete elastic wave-train in the interior domain obeying traction-free boundary conditions at the horizontal surface. More specifically, a special type of material inhomogeneity is studied, where the shear modulus varies quadratically with respect to the depth coordinate. Furthermore, the material density profile varies proportionally to the aforementioned profile, while Poisson's ratio remains fixed at one-quarter. Limit forms for the Green's functions are derived for both zero frequency and for the equivalent homogeneous medium. Next, a series of numerical results serve to validate this mechanical model, and to show the differences in the wave motion patterns developing in media that are inhomogeneous as compared to a reference homogeneous background. These singular solutions are useful within the context of boundary element formulations for the numerical solution of problems involving nonhomogeneous continua, which find applications in fields as diverse as composite materials, geophysical prospecting, petroleum exploration and earthquake engineering.

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“…This path was followed for the homogeneous case, i.e., a = 0 and with F(t) = 1, in [Guan et al 1998]. …”

Section: Time-harmonic Elastodynamic Green's Function For the Half-plmentioning

confidence: 99%

Section: Introduction and Problem Statementmentioning

confidence: 99%

Time-harmonic elastodynamic Green’s function for the half-plane modeled by a restricted inhomogeneity of quadratic type

Rangelov

Manolis

2010

J. Mech. Mater. Struct.

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“…A transient Green function for half-space response to suddenly applied line loads was developed by Guan et al [15]. It can be used in transient elastodynamic problems without modeling of the free surface.…”

Section: Introductionmentioning

confidence: 99%

Far-field dynamic behavior of a half-space under an inertial strip foundation subjected to a time-harmonic force

Dehestani

Malidarreh

Choobbasti

et al. 2013

Lat. Am. j. solids struct.

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Recent research works demonstrated that the interaction between the loads and the carrying structure's boundary which is related to the inertia of the load is an influential factor on the dynamic response of the structure. Although effects of the inertia in moving loads were considered in many works, very few papers can be found on the inertial effects of the stationary loads on structures. In this paper, an elastodynamic formulation was employed to investigate the dynamic response of a homogeneous isotropic elastic half-space under an inertial strip foundation subjected to a time-harmonic force. Fourier integral transformation was used to solve the system of Poisson-type partial differential equation considering the boundary conditions and the inertial effects. Steepest descent method was employed to obtain the approximate far-field displacements and stresses. A numerical example is presented to illustrate the methodology and typical results.

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“…The results from the frame model were compared with those given by the 2D finite element solution, and a good agreement was found. Guan et al [43] presented a transient Green function caused by suddenly applied line loads in an isotropic and homogeneous halfspace. Dineva and Manolis [44,45] developed a hybrid integral equation, based on both displacement and hypersingular traction formulations, for the analysis of timeharmonic seismic waves propagating through cracked, multi-layered geological regions with surface topography under plane strain conditions.…”

Section: Introductionmentioning

confidence: 99%

3D seismic response of a limited valley via BEM using 2.5D analytical Green's functions for an infinite free-rigid layer

António

Tadeu

2002

Soil Dynamics and Earthquake Engineering

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This paper presents analytical solutions for computing the 3D displacements in a flat solid elastic stratum bounded by a rigid base, when it is subjected to spatially sinusoidal harmonic line loads. These functions are also used as Greens functions in a boundary element method code that simulates the seismic wave propagation in a confined or semi-confined 2D valley, avoiding the discretization of the free and rigid horizontal boundaries.The models developed are then used to simulate wave propagation within a rigid stratum and valleys with different dimensions and geometries, when struck by a spatially sinusoidal harmonic vertical line load. Simulations are performed in the frequency domain, for varying spatial wave numbers in the axial direction of the valley. Time results are obtained by means of inverse Fourier transforms, to help understand how the geometry of the valley may affect the variation of the displacement field. q

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Two dimensional transient fundamental solution due to suddenly applied load in a half-space

Cited by 16 publications

References 11 publications

Time-harmonic elastodynamic Green’s function for the half-plane modeled by a restricted inhomogeneity of quadratic type

Time-harmonic elastodynamic Green’s function for the half-plane modeled by a restricted inhomogeneity of quadratic type

Far-field dynamic behavior of a half-space under an inertial strip foundation subjected to a time-harmonic force

3D seismic response of a limited valley via BEM using 2.5D analytical Green's functions for an infinite free-rigid layer

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