Three-dimensional dynamic Green’s functions for a multilayered transversely isotropic half-space

✍ Scribed by A. Khojasteh; M. Rahimian; M. Eskandari; R.Y.S. Pak

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 987 KB
• Volume: 48
• Category: Article
• ISSN: 0020-7683
• DOI: 10.1016/j.ijsolstr.2011.01.020

✦ Synopsis

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With the aid of a method of displacement potentials, an efficient and accurate analytical derivation of the three-dimensional dynamic Green's functions for a transversely isotropic multilayered half-space is presented. Constituted by proper algebraic factorizations, a set of generalized transmission-reflection matrices and internal source fields that are free of any numerically unstable exponential terms are proposed for effective computations of the potential solution. Three-dimensional point-load Green's functions for stresses and displacements are given, for the first time, in the complex-plane line-integral representations. The present formulations and solutions are analytically in exact agreement with the existing solutions given by for the isotropic case. For the numerical computation of the integrals, a robust and effective methodology which gives the necessary account of the presence of singularities including branch points and poles on the path of integration is laid out. A comparison with the existing numerical solutions for multilayered isotropic half-space is made to confirm the accuracy of the numerical solutions.