Elastodynamic Green’s functions of transversely isotropic n-layer half- and full-spaces subjected to a surface or buried time-harmonic annular loading and associated material degeneracy

• Published in: Journal of engineering mathematics Vol. 136; no. 1
• Main Authors: Soleimani, Kasra, Shodja, Hossein M., Rashidinejad, Ehsan
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.10.2022; Springer Nature B.V
• Subjects: Applications of Mathematics; Computational Mathematics and Numerical Analysis; Elastodynamics; Finite element method; Green's functions; Mathematical analysis; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Stress distribution; Theoretical and Applied Mechanics; Topology; Material degeneracy; Transversely isotropic; N-layer half-spaces and full-spaces; Elastodynamic Green’s functions; Surface and buried oblique time-harmonic
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-022-10237-4

The elastodynamic behavior of layered media consisting of an arbitrary combination of isotropic and transversely isotropic layers is of great importance for many engineering applications. In this work, some appropriate elastodynamic Green’s functions pertinent to both the displacement and the stress fields are devised so that the problems associated with the n-layer semi-infinite and infinite media with any combinations of transversely isotropic and isotropic layers subjected to surface and buried oblique time-harmonic annular loading can all be treated in a unified manner. The material degeneracy arising due to the scenarios where one or more regions are isotropic is also discussed and treated. The proposed Green’s functions are then utilized to address a number of illustrative examples involving different combinations of transversely isotropic and isotropic layers subjected to such loading conditions as point load, ring as well as full circularly distributed loads, and loading along a circle perimeter including normal, horizontal, and torsional type loads. The robustness of the current formulations is shown through the verification of the available results pertinent to several problems with diverse topologies and loading conditions. Additional examples which have not been addressed in the literature are also treated herein and verified either by using finite element analysis (FEA) or by considering the pertinent analytical limiting cases.