On stresses and displacements due to a moving line load over the plane boundary of a heterogeneous elastic half-space

Chakrabarty, S. K.; De, Tapan Kumar

doi:10.1007/bf00875409

Cited by 8 publications

(5 citation statements)

References 2 publications

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“…The propagation of Love waves in a homogeneous elastic layer supported on an inhomogeneous half-space 2 Chakrabarty and De [30] The stresses and displacements due to a concentrated line load moving with supersonic speed G(z) = G 0 (1+bz) 2 Gazetas [31] An analytical-numerical formulation is presented for dynamic displacements of strip foundations with Poisson's ratio = 0.25…”

Section: C-d Wang Et Almentioning

confidence: 99%

Wave propagation in an inhomogeneous cross‐anisotropic medium

Wang

Lin

Jeng

et al. 2009

Num Anal Meth Geomechanics

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SUMMARYAnalytical solutions for wave velocities and wave vectors are yielded for a continuously inhomogeneous cross-anisotropic medium, in which Young's moduli (E, E ) and shear modulus (G ) varied exponentially as depth increased. However, for the rest moduli in cross-anisotropic materials, and remained constant regardless of depth. We assume that cross-anisotropy planes are parallel to the horizontal surface. The generalized Hooke's law, strain-displacement relationships, and equilibrium equations are integrated to constitute governing equations. In these equations, displacement components are fundamental variables and, hence, the solutions of three quasi-wave velocities, V P , V SV , and V SH , and the wave vectors, l P l SV , and l SH , can be generated for the inhomogeneous cross-anisotropic media. The proposed solutions and those obtained by Daley and Hron, and Levin correlate well with each other when the inhomogeneity parameter, k, is 0. Additionally, parametric study results indicate that the magnitudes and directions of wave velocity are markedly affected by (1) the inhomogeneous parameter, k; (2) the type and degree of geomaterial anisotropy (E/E , G /E , and / ); and (3) the phase angle, . Consequently, one must consider the influence of inhomogeneous characteristic when investigating the behaviors of wave propagation in a cross-anisotropic medium.

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Section: C-d Wang Et Almentioning

confidence: 99%

Wave propagation in an inhomogeneous cross‐anisotropic medium

Wang

Lin

Jeng

et al. 2009

Num Anal Meth Geomechanics

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“…This free-field motion satisfies traction free boundary condition on x 2 = 0. The derivation of the analytical solutions (6), (7) for displacement and traction in the case of free-field motion is based, first, on the usage of the smooth transformation of the type, see [43]…”

Section: Problem Statementmentioning

confidence: 99%

“…Second, in order to obtain a solution of the transformed displacement the plane-wave decomposition method is applied, see [8]. Finally, applying the inverse transform in (8) we obtain the displacement (6) and correspondingly the traction (7).…”

Section: Problem Statementmentioning

confidence: 99%

“…We aim to solve this test example by using two different mechanical models accompanied by two different computational techniques based on Eqs. (6), (7), and (19), respectively. The equivalence of these two different approaches is shown in Figs.…”

Section: Test Examplementioning

confidence: 99%

“…Amplification factor at f = 1 Hz versus incident angle obtained analytically by Eqs. (6),(7) and by WNIM for the case of inhomogeneous in depth half-plane with inhomogeneous coefficient b = −0.5: (a) discrete model with 2 layers; (b) discrete model with 10 layers; (c) discrete model with 100 layers. Amplification factor at f = 1 Hz versus incident angle obtained analytically by Eqs.…”

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confidence: 99%

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SH‐wave propagation in a continuously inhomogeneous half‐plane with free‐surface relief by BIEM

et al. 2014

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The anti-plane strain elastodynamic problem for a continuously inhomogeneous half-plane with free-surface relief subjected to time-harmonic SH-wave is studied. The computational tool is a boundary integral equation method (BIEM) based on analytically derived Green's function for a quadratically inhomogeneous in depth half-plane. To show the versatility of the proposed BIE method, it is considered SH-wave propagation in an inhomogeneous half-plane with free surface relief presented by a semi-circle, semi-elliptic and triangle canyon. The inhomogeneous in depth half-plane is modeled in two different ways: (i) the material properties vary continuously in depth and BIEM based on Green's function is used; (ii) the material properties vary in a discrete way and the half-plane is presented by a set of homogeneous layers with horizontal interfaces and a hybrid technique based on wave number integration method (WNIM) and BIEM is applied. The equivalence of these two different models is shown. The simulations reveal a marked dependence of the wave field on the material inhomogeneity and the potential of the BIEM based on the Green's function for half-plane to produce highly accurate results by using strongly reduced discretization mesh in comparison with the conventional boundary element technique using fundamental solution for the full plane.

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Displacement produced in an elastic half-space by the impulsive torsional motion of a circular ring source

Ghosh

1980

PAGEOPH

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On stresses and displacements due to a moving line load over the plane boundary of a heterogeneous elastic half-space

Cited by 8 publications

References 2 publications

Wave propagation in an inhomogeneous cross‐anisotropic medium

Wave propagation in an inhomogeneous cross‐anisotropic medium

SH‐wave propagation in a continuously inhomogeneous half‐plane with free‐surface relief by BIEM

Displacement produced in an elastic half-space by the impulsive torsional motion of a circular ring source

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