Generalized characteristic method of elastodynamics
type: Item
instance of: scholarly article
title: Generalized characteristic method of elastodynamics
zbMATH Open document ID: 0848.73079
DOI: 10.1016/0020-7683(94)90179-1
author: S. G. Su
author: T. N. Farris
published in: International Journal of Solids and Structures
publication date: 1994-08-02T00:00:00Z
review text: A generalized characteristic method is developed to solve two-dimensional time-domain elastodynamic problems. It can be seen as the two-dimensional development of the method of characteristics analogous to d'Alembert's solution for one-dimensional problems. Using the solutions of two-dimensional elastodynamics problems in the complete \((x, y, t)\) space, the real characteristic surfaces are extended to the complex domains in which they are called generalized characteristics. Employing the expressions for stress components along the generalized characteristics, the initial-boundary value problems of elastodynamics can be reduced to a set of algebraic equations whose solutions are first order derivatives of the displacement components. The method leads directly to the reflection coefficients of elastic waves, whose fronts can be of arbitrary convex shape. The full plane Green's function is then found as the solution of a boundary value problem. The generalized characteristics are used directly to analyse the regions of reflected and head waves. The reflection coefficients and the full plane Green's function can be applied to the solution of Lamb's problem for a buried source. The solution yields particular compact expressions for the surface displacement and for subspace displacements induced by a surface force. Some numerical results are given for the displacement histories of receivers near and far from the source in the half-plane. The method can also be used in problems for transversely isotropic media and in problems of electromagnetic radiation.
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74J10
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 65M25
zbMATH DE Number: 612086
zbMATH Keywords: Navier's equations
zbMATH Keywords: Laplace transformation
zbMATH Keywords: Cagnard's technique
zbMATH Keywords: set of algebraic equations
zbMATH Keywords: reflection coefficients
zbMATH Keywords: plane Green's function
zbMATH Keywords: Lamb's problem
zbMATH Keywords: buried source
zbMATH Keywords: surface displacement
zbMATH Keywords: subspace displacements
MaRDI profile type: Publication
full work available at URL: 0020-7683(94)90179-1
OpenAlex ID: W2102495155
description: scientific article; zbMATH DE number 612086