An extendable poroelastic plate formulation in dynamics
A strategy is presented, which allows deriving poroelastic plate formulations of any desired level of approximation. Starting point are the governing three-dimensional (3D) equations of poroelasticity in frequency domain developed by Biot. In order to reduce the dimension of the problem from 3D to 2D, all unknown quantities are approximated by series expansions in thickness direction. This avoids the need for any engineering assumptions. The reduction in the dimension can then be achieved by an integration over the thickness. After truncating the series, a special plate formulation is retrieved. Results are presented for a square, clamped plate which show excellent agreement with the solution of the 3D equations and a considerable saving in computation time.
KeywordsPoroelasticity Biot’s theory Plate formulation Series expansion
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- 6.Bonnet G., Auriault J.L.: Dynamics of saturated and deformable porous media: homogenization theory and determination of the solid-liquid coupling coefficients, pp. 306–316. Springer, Berlin (1985) Physics of Finely Divided MatterGoogle Scholar
- 8.Cederbaum G., Li L., Schulgasser K.: Poroelastic structures. Elsevier Science, Amsterdam (2000)Google Scholar
- 9.Detournay, E., Cheng, A.H.D.: Fundamentals of poroelasticity, comprehensive rock engineering, vol. 2, pp. 113–171. Pergamon Pressm, Oxford (1993)Google Scholar
- 13.Kienzler, R.: On consistent second-order plate theories. In: Theories of plates and shells: critical review and new applications (Lecture Notes in Applied and Computational Mechanics), vol. 16, pp. 85–96. Springer (2004)Google Scholar