Boundary Element Formulation for Numerical Surface Wave Modelling in Poroviscoelastisity

Leonid A. Igumnov; Svetlana Litvinchuk; A.A. Belov; Aleksandr Ipatov

doi:10.4028/www.scientific.net/KEM.685.172

Paper Titles

Numerical Modeling of Cyclone Machine for Cleaning Gas Generator Gases
p.153

Simulation of Conditions of Solid Fossil Fuels Formation for Underground Conversion Investigation
p.158

Numerical Study of Grain Evolution and Dislocation Density during Asymmetric Rolling of Aluminum Alloy 7075
p.162

The End-to-End Computer Simulation of Casting and Subsequent Metal Forming
p.167

Boundary Element Formulation for Numerical Surface Wave Modelling in Poroviscoelastisity
p.172

Use of Lagrangian-Eulerian Computing Method for Systems with Phase Change at the Solution of Stefan Boundary Value Problem
p.177

Finite Element Modeling of Influence of Roll Form of Vertical Scale Breaker on Decreased Formation of Surface Defects during Roughing Hot Rolling
p.181

Mathematical Simulation of Cramped Bending of Sheet Parts Using Finite Element Analysis
p.186

Accounting Viscous Dissipation at Round Tubes Filling
p.191

HomeKey Engineering MaterialsKey Engineering Materials Vol. 685Boundary Element Formulation for Numerical Surface...

Boundary Element Formulation for Numerical Surface Wave Modelling in Poroviscoelastisity

Abstract:

Problems of the poroviscodynamics are considered. Theory of poroviscoelasticity is based on Biot’s equations of fluid saturated porous media under assumption that the skeleton is viscoelastic. Viscoelastic effects of solid skeleton are modeled by mean of elastic-viscoelastic correspondence principle, using such viscoelastic models as a standard linear solid model and model with weakly singular kernel. The fluid is taken as original in Biot’s formulation without viscoelastic effects. Boundary integral equations method is applied to solve three-dimensional boundary-value problems. Boundary-element method with mixed discretization and matched approximation of boundary functions is used. Solution is obtained in Laplace domain, and then Durbin’s algorithm of numerical inversion of Laplace transform is applied to perform solution in time domain. An influence of viscoelastic parameters on dynamic responses is studied. Numerical example of the surface waves modelling is considered.

You might also be interested in these eBooks

High Technology: Research and Applications 2015

View Preview

Info:

Periodical:

Key Engineering Materials (Volume 685)

Pages:

172-176

DOI:

https://doi.org/10.4028/www.scientific.net/KEM.685.172

Citation:

Cite this paper

Online since:

February 2016

Authors:

Leonid A. Igumnov, Svetlana Litvinchuk, A.A. Belov, Aleksandr Ipatov*

Keywords:

Boundary Element Method (BEM), Poroviscoelasticity, Rayleigh Surface Wave, Viscoelastic Models

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

* - Corresponding Author

References

[1] M.A. Biot General theory of three dimensional consolidation, J. Appl. Phys. 12. (1941) 155-164.

Google Scholar

[2] M.A. Biot Theory of propagation of elastic waves in a fluid-suturated porous solid, J. Acust. Soc. Amer. 28. (1956) 168-191.

Google Scholar

[3] M.A. Biot Theory of deformation of a porous viscoelastic anisotropic solid. J. Appl. Phys. 27. (1956) 459-467.

DOI: 10.1063/1.1722402

Google Scholar

[4] M. Schanz, Wave Propagation in Viscoelastic and Poroelastic Continua, Springer: Berlin, (2001).

Google Scholar

[5] T. A. Cruze, F. J. Rizzo, A direct formulation and numerical solution of the general transient elastodynamic problem, J. Math. Anal. Appl 22(1) (1968) 244.

Google Scholar

[6] V.G. Bazhenov, L.A. Igumnov, Boundary Integral Equations & Boundary Element Methods in treating the problems of 3D elastodynamics with coupled fields, PhysMathLit, Moscow, 2008. (In Russia).

Google Scholar

[7] A.G. Ugodchikov, N.M. Hutoryanskii, Boundary element method in deformable solid mechanics, Kazan State University, Kazan, 1986. (In Russia).

Google Scholar

[8] R. Cristensen Introduction to the theory of viscoelasticity, Mir, Moscow, 1974. (In Russia).

Google Scholar

[9] F. Durbin, Numerical inversion of Laplace transforms: an efficient improvement to Dubner and Abate's method, The Computer Journal. 17, (1974) 371–376.

DOI: 10.1093/comjnl/17.4.371

Google Scholar