A simplified model for elastic thin shells

TL;DR

This paper presents a simplified elastic energy model for thin shells that always admits minimizers and accurately predicts the behavior of the full model as shell thickness approaches zero.

Contribution

It introduces a new simplified model for thin shells that remains well-posed and aligns with the full model in the thin limit, unlike previous models.

Findings

The simplified model always admits minimizers.

The model's minimum converges to the full model's infimum as thickness tends to zero.

The approach is validated by asymptotic consistency with the original model.

Abstract

We introduce a simplified model for the minimization of the elastic energy in thin shells. This model is not obtained by an asymptotic analysis. The thickness of the shell remains a parameter as in Reisner-Mindlin's model for plates and Koiter's model for shells in the linear case. The simplified model admits always minimizers by contrast with the original one. We show the relevance of our approach by proving that the minimum of the simplified model and the infimum of the full model have the same limit as the thickness tends to 0.