Laplace Domain Boundary Element Method for 3D Poroelastodynamics

Abstract:

To describe poroelastic properties, a dynamic model of Biot’s material is used in the frame of the three-dimensional isotropic linear dynamic poroelasticity with four basic functions – displacements of the elastic skeleton and pore pressures. A direct version of the BIE method is developed. The boundary-element scheme is constructed using: regularized BIE’s, a matched element-by-element approximation, adaptive numerical integration in combination with a singularity-reducing algorithm, etc. The computer simulation is done using the boundary-element methodologies of the stepped method.

• Periodical: Applied Mechanics and Materials (Volume 709)
• Pages: 117-120
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.709.117
• Online since: December 2014
• Authors: Leonid A. Igumnov, Andrey Petrov*, Alexander V. Amenitskiy
• Keywords: 3D, BEM, Durbin’s Method, Dynamic, Poroelasticity

References

[1] Frenkel Ya.I. On the theory of seismic and seismic-electric phenomena in damp soils / Ya.I. Frenkel / News of AS USSR. Ser. Geography and Geophys. – 1944. – V. 8., № 4. – P. 65-78.

[2] Biot, M Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range / M. Biot / J. Acoust. Soc. Am. – 1956. V. 28, № 2. – P. 168-178.

DOI: 10.1121/1.1908239

[3] Biot, M Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher-frequency range / M. Biot / J. Acoust. Soc. Am. – 1956. V. 28, № 2. – P. 179-191.

DOI: 10.1121/1.1908241

[4] Schanz, M. Wave Propogation in Viscoelastic and Poroelastic Continua / M. Schanz. – Berlin Springer, 2001. – 170 p.

DOI: 10.1007/978-3-540-44575-3

[5] Manolis G.D., Beskos D.E. Integral Formulation and Fundamental Solutions of Dynamic Poroelasticity and Thermoelasticity / Ada Mechanica. 1989. № 76. P. 89-104.

DOI: 10.1007/bf01175798

[6] Аmenitskiy А.V., Belov А.А., Igumnov L.А., Каrelin I.S. Boundary integral equations for analyzing dynamic problems of three-dimensional poroelasticity. Inter- University collection. Problems of strength and plasticity. N. Novgorod, NNSU Publishers, 2009, Issue. 71, P. 164-171.

DOI: 10.32326/1814-9146-2009-71-1-164-171

[7] Belov А.А., Igumnov L.А., Каrelin I.S., Litvinchuk S. Yu. Application of the BIE-method for analyzing boundary-value problems of three-dimensional dynamic visco- and poroelasticity / Electronic Journal «Proc. of MAI ». 2010. Issue № 40. P. 1-20. (in Russian).

[8] Bazhenov V.G., Igumnov L.А. Boundary integral equation and boundary-element methods in the analyses of 3-D problems of dynamic elasticity with coupled fields. М.: Fizzmatlit, 2008. – 352 p. (in Russian).

[9] Durbin, F. Numerical inversion of Laplace transforms: an efficient improvement to Dubner and Abate's method / Durbin F. / The Computer Journal. – 1974. – Vol. 17, 4. – P. 371–376. (in Russian).

DOI: 10.1093/comjnl/17.4.371