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.
On Variational Dimension Reduction in Structure Mechanics
Paroni, Roberto;
2015-01-01
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 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
