Porous Media Analysis by Modified MLPG Formulations
D. Soares Jr.; V. Sladek; J. Sladek; M. Zmindak; S. Medvecky

Source CMC: Computers, Materials & Continua, Vol. 27, No. 2, pp. 101-127, 2012
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Keywords Meshless Local Petrov-Galerkin; Moving Least Squares; Analytical Integration; Shape Function Derivatives; Poroelastodynamics; Independent Phase Discretization.
Abstract This work proposes a modified procedure, based on analytical integrations, to analyse poroelastic models discretized by time-domain Meshless Local Petrov-Galerkin formulations. In this context, Taylor series expansions of the incognita fields are considered, and the related integrals of the meshless formulations are solved analytically, rendering a so called modified methodology. The work is based on the u-p formulation and the incognita fields of the coupled analysis in focus are the solid skeleton displacements and the interstitial fluid pore pressures. Independent spatial discretization is considered for each phase of the model, rendering a more flexible and efficient methodology. The Moving Least Squares approximation is employed for the spatial variation of the displacement and pore-pressure fields and two variants of the meshless local Petrov-Galerkin formulation are discussed here, which are based on the use of Heaviside or Gaussian weight test functions. Modified expressions to properly compute the shape function derivatives are also considered. At the end of the paper, numerical examples illustrate the performance and potentialities of the proposed techniques.
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