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arXiv · 1305.3170

On variational dimension reduction in structure mechanics

Roberto Paroni·Paolo Podio-Guidugli
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Abstract

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 re- duction 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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Roberto Paroni, Paolo Podio-Guidugli. 2013-05-14. On variational dimension reduction in structure mechanics. https://arxiv.org/abs/1305.3170

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