Abstract
The present paper is dedicated to dynamic behavior of poroelastic solids. Biot’s model of poroelastic media with four base functions is employed in order to describe wave propagation process, base functions are skeleton displacements and pore pressure of the fluid filler. In order to study the boundary-value problem boundary integral equations (BIE) method is applied, and to find their solutions boundary element method (BEM) for obtaining numerical solutions. The solution of the original problem is constructed in Laplace transforms, with the subsequent application of the algorithm for numerical inversion. The numerical scheme is based on the Green-Betty-Somigliana formula. To introduce BE-discretization, we consider the regularized boundary-integral equation. The collocation method is applied. As a result, systems of linear algebraic equations will be formed and can be solved with the parallel calculations usage. Modified Durbin’s algorithm of numerical inversion of Laplace transform is applied to perform solution in time domain. A problem of the three-dimensional poroelastic prismatic solid clamped at one end, and subjected to uniaxial and uniform impact loading and a problem of poroelastic cube with cavity subjected to a normal internal pressure are considered.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Frenkel, J.: On the theory of seismic and seismoelectric phenomena in a moist soil. J. Phys. 8, 230–241 (1944)
Biot, M.A.: Theory of propagation of elastic waves in a fluid-suturated porous solid. J. Acoust. Soc. Am. 28(2), 168–191 (1956)
Schanz, M.: Poroelastodynamics: linear models, analytical solutions, and numerical methods. Appl. Mech. Rev. 62(3), 030803-1–030803-15 (2009)
Schanz, M.: Wave Propagation in elastic and Poroelastic Continua. Springer, Berlin (2001)
Cruze, T.A., Rizzo, F.J.: A direct formulation and numerical solution of the general transient elastodynamic problem I. J. Math. Anal. Appl. 22(1), 244–259 (1968)
Ugodchikov, A.G., Hutoryanskii, N.M.: Boundary element method in deformable solid mechanics. Kazan State University, Kazan (1986)
Durbin, F.: Numerical inversion of Laplace transforms: an efficient improvement to Dubner and Abate’s method. Comput. J. 17(4), 371–376 (1974)
Zhao, X.: An efficient approach for the numerical inversion of Laplace transform and its application in dynamic fracture analysis of a piezoelectric laminate. Int. J. Solids Struct. 41, 3653–3674 (2004)
Acknowledgements
This work was supported by a grant from the Government of the Russian Federation (contract No. 14.Y26.31.0031).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Igumnov, L., Litvinchuk, S., Ipatov, A., Iuzhina, T. (2019). The Boundary-Element Approach to Modeling the Dynamics of Poroelastic Bodies. In: Gdoutos, E. (eds) Proceedings of the Second International Conference on Theoretical, Applied and Experimental Mechanics. ICTAEM 2019. Structural Integrity, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-030-21894-2_57
Download citation
DOI: https://doi.org/10.1007/978-3-030-21894-2_57
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-21893-5
Online ISBN: 978-3-030-21894-2
eBook Packages: EngineeringEngineering (R0)