We briefly review the Green's function method for solution of the Christoffel equation and a computationally efficient method for calculating the Green's function for
anisotropic solids. We describe the virtual-force method for satisfying the boundary conditions to account for scontinuities in the solids. The virtual-force method consists of applying a
distribution of virtual forces just outside the domain of solution. The solution obtained by using the virtual-force distribution and the Green's function gives a solution of the homogeneous
equation. The virtual-force distribution is then determined by imposing the prescribed boundary conditions. This method is similar to the image-charge method in electrostatics [1] and is the basis
for the boundary-element method [2] for solving elastodynamic problems. The Fourier representation of the Green's function is quite general and, subject to certain well-known conditions of
integrability and convergence [1], can be used for most physical problems. In the case of elastodynamic Green's functions, the Fourier representation is CPU intensive and is not computationally
efficient for anisotropic solids. We have developed a delta-function representation [3] that is particularly suitable for anisotropic solids. In this paper, we describe the delta-function
representation for elastodynamic as well as elastostatic Green's functions for infinite solids and its application to bounded solids by using the virtual- force method.
Date
1994-04-14
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Seminar Series
NIST workshop on Green’s functions and boundary element analysis
Institution
National Institute of Standards and Technology
Location
Boulder, Colorado
Copyright Agreement
on
Additional Notes
Proceedings of the NIST workshop on Green’s functions and boundary element analysis published as NIST Special Publication SP 910 (1996)
Guest - March 16, 2010
View Seminar Paper: Elastic Green's Functions for Anisotropic Solids 