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Mindlin theory for the bending of porous plates

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Abstract

Biot’s poroelastic theory has been applied for Mindlin plates to model moderately thick plates. If Mindlin’s kinematical assumptions and a power series expansion for the pore pressure in the thickness direction are considered, the original 3D problem is reduced to 2D. A truncated power series expansion with quadratic terms is considered for the pore pressure. Two functional relationships based on the given boundary conditions and one PDE are derived for the expansion coefficients. A meshless method based on the local Petrov–Galerkin approach is proposed to solve the set of governing PDE in the neutral plane of the poroelastic plate. All in-plane quantities are approximated by the moving least-squares scheme. After performing the spatial integrations, one obtains a system of ordinary differential equations for certain nodal unknowns.

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Authors and Affiliations

  1. Institution of Construction and Architecture, Slovak Academy of Sciences, 84503, Bratislava, Slovakia

    J. Sladek & V. Sladek

  2. Institute of Applied Mechanics, Graz University of Technology, Graz, Austria

    M. Gfrerer & M. Schanz

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  1. J. Sladek
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  2. V. Sladek
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  3. M. Gfrerer
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  4. M. Schanz
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Correspondence to J. Sladek.

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Sladek, J., Sladek, V., Gfrerer, M. et al. Mindlin theory for the bending of porous plates. Acta Mech 226, 1909–1928 (2015). https://doi.org/10.1007/s00707-014-1287-x

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  • DOI: https://doi.org/10.1007/s00707-014-1287-x

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