Causality condition relevant functions-orientated analytical treatment on singularities in 3D TD-BEM

Lei, Weidong; Qin, Xiaofei; Li, Hongjun; Fan, Yun

doi:10.1016/j.amc.2022.127113

Cited by 3 publications

(1 citation statement)

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“…With their common role as the key kernels in convolution-type time-domain integral formulations for general initial-boundary value problems for instance, inadequate accounts of their singular aspects can lead not only to a loss of accuracy but also stability issues in the solution algorithms (e.g. Bai & Pak [12], Lei et al [13]).…”

Section: Introductionmentioning

confidence: 99%

Unified wavefront singularity characterization of three-dimensional elastodynamic time-domain half-space Green's function under impulsive boundary and internal loads

Pak,

Bai

2024

Proc. R. Soc. A.

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Founded on a novel analytical formulation that led to a rigorous yet compact path-integral representation of the time-domain elastodynamic half-space Green's function, a unified analysis of the possible occurrence of different singular wavefront behaviour in the response under arbitrary impulsive internal or surface point loads at arbitrary source-receiver locations is presented. With the decomposition of the general solution into distinct initiating and reflected wave group integrals that share a common factored format and simple contour definitions, the mathematical framework is shown to allow a straightforward identification of the specific conditions and the particular wave groups that are responsible for the singular wavefront phenomena without resorting to advanced analytic function theories or asymptotic methods. Analytic characterizations of the nature, strength and direction of all intrinsic singular wavefront behaviours of the three-dimensional Green's function in three canonical cases of source-receiver configurations are given in a dual integral-closed form format to facilitate their theoretical understanding as well as computational applications. Graphical illustrations of their variation with the source-receiver configuration and the medium's Poisson's ratio together with relevant comparison and clarifications of some classical treatments are included.

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Section: Introductionmentioning

confidence: 99%