Mathematical boundary integral equation analysis of an embedded shell under dynamic excitations

Pak, Ronald Y. S.; Jiao, Feng

doi:10.1002/nme.1620371409

Cited by 35 publications

(14 citation statements)

References 14 publications

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“…[19,24]), the singularity induced by the Rayleigh pole is one for which a similar approach or densified numerical quadrature as in [24] is generally ineffective. For a rigorous analytical and numerical treatment of such aspects, the method of asymptotic decomposition [28] for delineating complicated dynamic and static singular fundamental solutions (see [29,30,38,39] for details) can be extended to the time domain to resolve the issue. Expressed in the equation form of present [23] present [23] present [23] present [23] present [23] present [23] present [23] present [23] present…”

Section: Numerical Implementation and Illustrative Resultsmentioning

confidence: 99%

Analytic resolution of time-domain half-space Green's functions for internal loads by a displacement potential-Laplace-Hankel-Cagniard transform method

Pak

Bai

2020

Proc. R. Soc. A.

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A refined yet compact analytical formulation is presented for the time-domain elastodynamic response of a three-dimensional half-space subject to an arbitrary internal or surface force distribution. By integrating Laplace and Hankel transforms into a method of displacement potentials and Cagniard's inversion concept, it is shown that the solution can be derived in a straightforward manner for the generalized classical wave propagation problem. For the canonical case of a buried point load with a step time function, the response is proved to be naturally reducible with the aid of a parametrized Bessel function integral representation to six wave-group integrals on finite contours in the complex plane that stay away from all branch points and the Rayleigh pole except possibly at the starting point of the contours. On the latter occasions, the possible singularities of the integrals can be rigorously extracted by an extended method of asymptotic decomposition, rendering the residual numerical computation a simple exercise. With the new solution format, the arrival time of each wave group is derivable by simple criteria on the contour. Typical results for the time-domain response for an internal point force as well as the degenerate case of a surface point source are included for comparison and illustrations.

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Section: Numerical Implementation and Illustrative Resultsmentioning

confidence: 99%

Analytic resolution of time-domain half-space Green's functions for internal loads by a displacement potential-Laplace-Hankel-Cagniard transform method

Pak

Bai

2020

Proc. R. Soc. A.

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“…In order to compute the IHT integrals, the integrands may be split into a strong decaying term plus a term which is integrated in closed-form, which represents the singular component. The leading asymptotic expansions (see Pak, 1987;Pak and Ji, 1994) of the displacements and traction functions are termed v a im ðf; zÞ and r a ij m ðf; zÞ. The components of v a im ðfÞ may be factorised as follows:…”

Section: Asymptotic Decompositionmentioning

confidence: 99%

Three-dimensional Green’s function for time-harmonic dynamics in a viscoelastic layer

Martínez-Castro

Gallego

2007

International Journal of Solids and Structures

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This paper presents Green's function for time-harmonic elastodynamic problems for a single layer domain (three-dimensional region bounded by two parallel planes with traction-free boundary conditions). The semi-analytic solution is built in three steps: (a) potential displacement representation; (b) angular Fourier series; (c) radial Hankel transform. Reflection matrices are presented for the plate domain. Kernels are integrally split into a singular closed-form term (the static half-space solution) plus an incremental solution. In order to compute the inverse Hankel transform for displacements and stress components, a modified complex integration path is required. Theoretical considerations allow an adequate delimitation of such a complex path. A specific treatment is proposed for low excitation frequencies where asymmetric Lamb waves play a major role. A series of numerical benchmarks are presented to validate the implementation of the functions (displacements and tractions).

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“…Later, in a more developed and accurate form for elastic piles under axial load by Pak and Ji [11] and lateral loads by Abedzadeh and Pak [12] and [13] are presented in the literature. Also, dynamic soil-pile interaction was the subject of such analysis and for cylindrical thin-walled piles in isotropic media can be found in Pak and Ji [14] and Ji and Pak [15].…”

Section: Introductionmentioning

confidence: 99%

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

Shahmohamadi

Khojasteh

Rahimian

et al. 2011

Num Anal Meth Geomechanics

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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.

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Mathematical boundary integral equation analysis of an embedded shell under dynamic excitations

Cited by 35 publications

References 14 publications

Analytic resolution of time-domain half-space Green's functions for internal loads by a displacement potential-Laplace-Hankel-Cagniard transform method

Analytic resolution of time-domain half-space Green's functions for internal loads by a displacement potential-Laplace-Hankel-Cagniard transform method

Three-dimensional Green’s function for time-harmonic dynamics in a viscoelastic layer

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

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