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摘要
In this work, smoothed meshfree methods are firstly applied to numerically analyze nonlinear pore-dynamic models. A weakened weak formulation based on the edges of triangular cells obtained by a Delaunay triangulation is considered here, framing the so-called edge-based smoothed domains. The meshfree shape functions are computed by the radial point interpolation method considering the T6-scheme for the shape function support domains. Enhanced procedures to compute the mass, compressibility and coupling matrices of the pore-dynamic model are discussed, which are consistent with the computation of the stiffness and permeability matrices (as well as internal force vectors, in case of nonlinear analyses) of the edge-based smoothed domain formulation and that consider finer local integration techniques at lower computational costs, rendering more accurate and efficient procedures. Two numerical formulations are considered here to analyze the time-domain nonlinear coupled system of equations that arises once the spatial discretization is accomplished: the standard Newmark/Newton-Raphson method and an alternative iterative coupling approach. In this iterative approach, each phase of the coupled problem is treated separately, uncoupling the governing equations of the model; thus, smaller and better conditioned systems of equations are obtained, rendering more attractive techniques. A relaxation parameter is introduced in order to improve the efficiency of the iterative coupling procedure and an expression to compute optimal values for the relaxation parameter is discussed. At the end of the paper, numerical examples are presented, illustrating the effectiveness and potentialities of the proposed methodologies.
- 出版日期2013-1-1
