Paroni, Roberto and Podio-Guidugli, Paolo (2015) On variational dimension reduction in structure mechanics. Journal of Elasticity, Vol. 118 (1), p. 1-13. ISSN 0374-3535. eISSN 1573-2681. Article.
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The classical low-dimensional models of thin structures are based on certain a priori assumptions on the three-dimensional deformation and/or stress fields, diverse in nature but all motivated by the smallness of certain dimensions with respect to others. In recent years, a considerable amount of work has been done in order to rigorously justify these a priori assumptions; in particular, several techniques have been introduced to make dimension reduction rigorous. We here review, and to some extent reformulate, the main ideas common to these techniques, using some explicit dimension-reduction problems to exemplify the points we want to make.
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