Browsing by Author "Madureira, Alexandre L."

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    Asymptotic estimates of hierarchical modeling
    (2003-10) Arnold, Douglas N.; Madureira, Alexandre L.
    In this paper we propose a way to analyze certain classes of dimension reduction models for elliptic problems in thin domains. We develop asymptotic expansions for the exact and model solutions, having the thickness as small parameter. The modeling error is then estimated by comparing the respective expansions, and the upper bounds obtained make clear the influence of the order of the model and the thickness on the convergence rates. The techniques developed here allows for estimates in several norms and semi-norms, and also interior estimates (which disregards boundary layers).
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    On the range of applicability of the Reissner-Mindlin and Kirchhoff-Love plate bending models
    (2002-08) Arnold, Douglas N.; Madureira, Alexandre L.; Zhang, Sheng
    We show that the Reissner-Mindlin plate bending model has a wider range of applicability than the Kirchhoff-Love model for the approximation of clamped linearly elastic plates. Under the assumption that the body force density is constant in the transverse direction, the Reissner-Mindlin model solution converges to the three-dimensional linear elasticity solution in the relative energy norm for the full range of surface loads. However, for loads with a significant transverse shear effect, the Kirchhoff-Love model fails.