caa a22 4500 60551531X CHVBK 20210128100708.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s00205-014-0805-2 doi (NATIONALLICENCE)springer-10.1007/s00205-014-0805-2 A Rigorous Derivation of the Equations for the Clamped Biot-Kirchhoff-Love Poroelastic Plate [Elektronische Daten] [Anna Marciniak-Czochra, Andro Mikelić] In this paper we investigate the limit behavior of the solution to quasi-static Biot's equations in thin poroelastic plates as the thickness tends to zero. We choose Terzaghi's time corresponding to the plate thickness and obtain the strong convergence of the three-dimensional solid displacement, fluid pressure and total poroelastic stress to the solution of the new class of plate equations. In the new equations the in-plane stretching is described by the two dimensional Navier's linear elasticity equations, with elastic moduli depending on Gassmann's and Biot's coefficients. The bending equation is coupled with the pressure equation and it contains the bending moment due to the variation in pore pressure across the plate thickness. The pressure equation is parabolic only in the vertical direction. As additional terms it contains the time derivative of the in-plane Laplacian of the vertical deflection of the plate and of the elastic in-plane compression term. Springer-Verlag Berlin Heidelberg, 2014 Marciniak-Czochra Anna Institute of Applied Mathematics, IWR and BIOQUANT, University of Heidelberg, Im Neuenheimer Feld 267, 69120, Heidelberg, Germany aut Mikelić Andro Université de Lyon, CNRS UMR 5208, Université Lyon 1, Institut Camille Jordan, 43, blvd. du 11 novembre 1918, 69622, Villeurbanne Cedex, France aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 215/3(2015-03-01), 1035-1062 0003-9527 215:3<1035 2015 215 205 https://doi.org/10.1007/s00205-014-0805-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-014-0805-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Marciniak-Czochra Anna Institute of Applied Mathematics, IWR and BIOQUANT, University of Heidelberg, Im Neuenheimer Feld 267, 69120, Heidelberg, Germany aut NATIONALLICENCE 700 1- Mikelić Andro Université de Lyon, CNRS UMR 5208, Université Lyon 1, Institut Camille Jordan, 43, blvd. du 11 novembre 1918, 69622, Villeurbanne Cedex, France aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 215/3(2015-03-01), 1035-1062 0003-9527 215:3<1035 2015 215 205