Weak forms for modelling of rotationally symmetric, multilayered structures, including anisotropic poro-elastic media
2012 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 90, no 8, 1035-1052 p.Article in journal (Refereed) Published
A weak form of the anisotropic Biot's equation represented in a cylindrical coordinate system using a spatial Fourier expansion in the circumferential direction is presented. The original three dimensional Cartesian anisotropic weak formulation is rewritten in an arbitrary orthogonal curvilinear basis. Introducing a cylindrical coordinate system and expanding the circumferential wave propagation in terms of orthogonal harmonic functions, the original, geometrically rotationally symmetric three dimensional boundary value problem, is decomposed into independent two-dimensional problems, one for each harmonic function. Using a minimum number of dependent variables, pore pressure and frame displacement, a computationally efficient procedure for vibro-acoustic finite element modelling of rotationally symmetric three-dimensional multilayered structures including anisotropic porous elastic materials is thus obtained. By numerical simulations, this method is compared with, and the correctness is verified against, a full three-dimensional Cartesian coordinate system finite element model.
Place, publisher, year, edition, pages
John Wiley & Sons, 2012. Vol. 90, no 8, 1035-1052 p.
Biot’s equations, cylindrical coordinates, porous media, Fourier expansion, weak formulation, anisotropic
IdentifiersURN: urn:nbn:se:kth:diva-82497DOI: 10.1002/nme.3354ISI: 000303113500005ScopusID: 2-s2.0-84860258278OAI: oai:DiVA.org:kth-82497DiVA: diva2:498292
FunderTrenOp, Transport Research Environment with Novel Perspectives
QC 20120524. Accepted 5 October 2011. Manuscript ID: NME-Mar-11-0185.R1- QS 20122012-02-122012-02-122013-04-10Bibliographically approved