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Wave Propagation in Viscoelastic and Poroelastic Continua A Boundary Element Approach

In this book, a numerical method to treat wave propagation problems in poroelastic and viscoelastic media is developed and evaluated. The method of choice is the Boundary Element Method (BEM) since this method implicitly fulfills the Sommerfeld radiation condition. The crucial point in any time-depe...

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Bibliographic Details
Main Author: Schanz, Martin
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2001, 2001
Edition:1st ed. 2001
Series:Lecture Notes in Applied and Computational Mechanics
Subjects:
Mechanics, Applied
Classical Mechanics
Numerical Analysis
Solids
Solid Mechanics
Mechanics
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 1. Introduction
  • 2. Convolution quadrature method
  • 2.1 Basic theory of the convolution quadrature method
  • 2.2 Numerical tests
  • 3. Viscoelastically supported Euler-Bernoulli beam
  • 3.1 Integral equation for a beam resting on viscoelastic foundation
  • 3.2 Numerical example
  • 4. Time domain boundary element formulation
  • 4.1 Integral equation for elastodynamics
  • 4.2 Boundary element formulation for elastodynamics
  • 4.3 Validation of proposed method: Wave propagation in a rod
  • 5. Viscoelastodynamic boundary element formulation
  • 5.1 Viscoelastic constitutive equation
  • 5.2 Boundary integral equation
  • 5.3 Boundary element formulation
  • 5.4 Validation of the method and parameter study
  • 6. Poroelastodynamic boundary element formulation
  • 6.1 Biot’s theory of poroelasticity
  • 6.2 Fundamental solutions
  • 6.3 Poroelastic Boundary Integral Formulation
  • 6.4 Numerical studies
  • 7. Wave propagation
  • 7.1 Wave propagation in poroelastic one-dimensional column
  • 7.2 Waves in half space
  • 8. Conclusions — Applications
  • 8.1 Summary
  • 8.2 Outlook on further applications
  • A. Mathematic preliminaries
  • A.1 Distributions or generalized functions
  • A.2 Convolution integrals
  • A.3 Laplace transform
  • A.4 Linear multistep method
  • B. BEM details
  • B.1 Fundamental solutions
  • B.1.1 Visco- and elastodynamic fundamental solutions
  • B.1.2 Poroelastodynamic fundamental solutions
  • B.2 “Classical” time domain BE formulation
  • Notation Index
  • References

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