Hierarchical Modeling of Heterogeneous Plates

A.C. Carius, A.L. Madureira


We describe here the modeling of highly heterogeneous plates, whenthree different lenght scales are present: the area of the middle surface, the platethickness, and the heterogeneity scale. We derive a two-dimensional PDE model forsuch problem, which turns out to have rough coefficients. We employ asymptotictechniques to estimate the modeling error with respect to the thickness. To tamethe numerical troubles of the resulting model we use finite elements methods ofmultiscale type.


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DOI: https://doi.org/10.5540/tema.2007.08.02.0219

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Trends in Computational and Applied Mathematics

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