Weak formulation of Biot's equations in cylindrical coordinates with harmonic expansion in the circumferential direction
2010 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 81, no 11, 1439-1454 p.Article in journal (Refereed) Published
A weak symmetric form of Biot's equation in cylindrical coordinates with a spatial Fourier expansion in the circumferential direction is presented. The solid phase displacement and the pore pressure are used as the dependent variables. The original three-dimensional boundary value problem is here, due to the orthogonality of the harmonic functions and the rotationally symmetric geometry, decomposed into independent two-dimensional problems, one for each harmonic function. This formulation provides a computationally efficient procedure for vibroacoustic finite element modelling of rotationally symmetric three-dimensional multilayered structures including porous elastic materials. By numerical Simulations, this method is compared with, and verified against, full three-dimensional Cartesian coordinate system finite element models.
Place, publisher, year, edition, pages
2010. Vol. 81, no 11, 1439-1454 p.
Biot's equations, cylindrical coordinates, porous material, Fourier, expansion, weak formulation, poroelastic materials, complex-modes
Engineering and Technology
IdentifiersURN: urn:nbn:se:kth:diva-19252DOI: 10.1002/nme.2739ISI: 000274925300004ScopusID: 2-s2.0-74949091356OAI: oai:DiVA.org:kth-19252DiVA: diva2:337299
QC 201005252010-08-052010-08-052012-05-22Bibliographically approved