Overview

Wave propagation in poroelastic and viscoelastic solids treated by the Boundary Element method in time domain is the topic of this research book. A novel boundary element formulation has been presented based on the Convolution Quadrature Method. Because in this time-stepping formulation only Laplace domain fundamental solutions are needed this method can be effectively applied to a plenty of problems, e.g. , anisotropic or transversely isotropic continua. So, this method combines the advantage of the Laplace domain with the advantage of a time domain calculation. Here, wave propagation phenomenon in viscoelastic as well as poroelastic half spaces are considered. The Rayleigh wave as well as the slow compressional wave in the poroelastic solid is discussed.

Full Product Details

Author:   Martin Schanz
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2001 ed.
Volume:   2
Dimensions:   Width: 15.50cm , Height: 1.20cm , Length: 23.50cm
Weight:   0.970kg
ISBN:  

9783540416326

ISBN 10:   3540416323
Pages:   170
Publication Date:   08 May 2001
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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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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