Abstract
The integral equation for the three-dimensional transient dynamics of an isotropic elastic medium has been known for about a century, and numerical methods for solving the equation have been under development for about a quarter-century. However, utilization of the integral equation in the development of non-reflecting computational boundaries has been impeded by the complexity of the integral operators and the unacceptable demands on computational resources. The state of development for anisotropic and layered media is much further behind
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References
P. Underwood and T.L. Geers, Doubly Asymptotic, Boundary-Element Analysis of Dynamic Soil-Structure Interaction. Int. J. Solids Struc, Vol. 17 (1981), pp. 687–697.
I.C. Mathews and T.L. Geers, A Doubly Asymptotic, Nonreflecting Boundary for Ground-Shock Analysis, J. Appl. Mech., Vol. 54 (1987), pp. 409–415.
T.L. Geers and B.A. Lewis, Doubly Asymptotic Nonreflecting Boundaries for Transient Elastodynamic Scattering, Proc. Int. Symp. on Boundary Element Methods, University of Colorado, Boulder (1992).
P.E. Grafton and J.W.L. Fox, Interaction of Ground Motion in an Elastic Medium with Buried Structures, AIAA Paper No. 64–410, AIAA Second Annual Meeting (1965)
T.L. Geers, Excitation of an Elastic Cylindrical Shell by a Transient Acoustic Wave, J. Appl. Mech., Vol. 36 (1969), pp. 459–469.
M.C. Junger and D. Feit, Sound, Structures and Their Interaction, MIT Press, Cambridge, MA (1986)
Y.-H. Pao and C.-C. Mow, Diffraction of Elastic waves and Dynamic Stress Concentrations, Rand Corp. Research Study (1972).
T.L. Geers, A.A. Oberai and C.-L. Yen, Excitation of a Spherical Shell in an Infinite Elastic Medium by a Transient Stress Wave, submitted for publication.
T.L. Geers and C.-L. Yen, C.-L., Transient Excitation of Cylindrical and Spherical Shells Embedded in an Elastic Medium: Residual Potential and Doubly Asymptotic Solutions, Proc. Tenth U.S. Nat’l Cong. Appl. Mech.(1986); also, LMSC-D767735, Lockheed Palo Alto Research Laboratory, Palo Alto, CA.
P. Zhang and T.L. Geers, Excitation of a Fluid Filled, Submerged Spherical Shell by a Transient Acoustic Wave, J. Acoust. Soc. Am., Vol. 93 (1992), pp. 696–705.
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© 1995 Springer-Verlag Berlin Heidelberg
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Geers, T.L., Oberai, A.A. (1995). An Evaluation of Doubly Asymptotic Boundaries for Transient Elastodynamics. In: Atluri, S.N., Yagawa, G., Cruse, T. (eds) Computational Mechanics ’95. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79654-8_510
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DOI: https://doi.org/10.1007/978-3-642-79654-8_510
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