Journal ArticleDOI
Propagation of Stress Discontinuities in Inhomogeneous Elastic Media
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This article is published in Siam Review.The article was published on 1964-10-01. It has received 31 citations till now. The article focuses on the topics: Stress (mechanics) & Classification of discontinuities.read more
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Book ChapterDOI
The Linear Theory of Elasticity
TL;DR: Linear elasticity is one of the more successful theories of mathematical physics and its pragmatic success in describing the small deformations of many materials is uncontested The origins of the three-dimensional theory go back to the beginning of the 19th century and the derivation of the basic equations by Cauchy, Navier, and Poisson The theoretical development of the subject continued at a brisk pace until the early 20th century with the work of Beltrami, Betti, Boussinesq, Kelvin, Kirchhoff, Lame, Saint-Venant, Somigl
Journal ArticleDOI
Solving two-point seismic-ray tracing problems in a heterogeneous medium. Part 1. A general adaptive finite difference method
TL;DR: In this article, a general numerical method to solve two-point seismic-ray tracing problems in a heterogeneous isotropic medium and how to solve them numerically is presented.
Journal ArticleDOI
Fast Seismic Ray Tracing
H. B. Keller,D. J. Perozzi +1 more
TL;DR: In this paper, a method for the fast, accurate and efficient calculation of large classes of seismic rays joining two points x+s and x_R in very general two-dimensional configurations is presented.
Journal ArticleDOI
Interfaces in micromorphic materials: Wave transmission and reflection with numerical simulations:
TL;DR: In this paper, the reflection and transmission of elastic waves at the interface between two distinct micromorphic media are considered in the one-dimensional setting, and a dual internal variable approach is used for th...
References
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Book
Methods of Mathematical Physics
Richard Courant,David Hilbert +1 more
TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.
Journal ArticleDOI
Geometrical Theory of Diffraction
TL;DR: The mathematical justification of the theory on the basis of electromagnetic theory is described, and the applicability of this theory, or a modification of it, to other branches of physics is explained.
Journal ArticleDOI
Elastic Wave Propagation in Homogeneous and Inhomogeneous Media
Frank C. Karal,Joseph B. Keller +1 more
TL;DR: In this paper, a general method is developed for the solution of the linearized equations of elasticity for both homogeneous and inhomogeneous media, which yields solutions which describe propagating waves which may be pulses, rapidly changing wave forms, or periodic waves.