Premium
Weak formulation of Biot's equations in cylindrical coordinates with harmonic expansion in the circumferential direction
Author(s) -
Östberg M.,
Hörlin N. E.,
Göransson P.
Publication year - 2009
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2739
Subject(s) - biot number , cartesian coordinate system , mathematical analysis , cylindrical coordinate system , finite element method , orthogonal coordinates , fourier series , spherical harmonics , generalized coordinates , geometry , harmonic , mathematics , harmonic function , spherical coordinate system , coordinate system , boundary value problem , orthogonality , bipolar coordinates , physics , mechanics , quantum mechanics , thermodynamics
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. Copyright © 2009 John Wiley & Sons, Ltd.