Homogenized moderately wrinkled shell theory from 3D Koiter's linear elasticity

TL;DR

This paper derives homogenized shell models from 3D linear elasticity for moderately wrinkled shells using two-scale convergence, revealing different theories depending on the small parameter and periodic wrinkling behavior.

Contribution

It introduces a homogenized shell theory for moderately wrinkled shells derived from 3D elasticity, considering the effects of periodic wrinkling and small parameters.

Findings

Derived shell models depend on the small parameter and wrinkling behavior.

Established a connection between 3D elasticity and shell theories through homogenization.

Identified different limiting theories based on the parameter regimes.

Abstract

In this paper we derive, by two$-$scale convergence, periodically wrinked shell models starting from three dimensional linear elasticity, depending of the behaviour of the small parameter $\varepsilon>0$ and $p>1$, differents theories appear. We assume that the mid-surface of the shell is given by $\displaystyle \psi(x_1,x_2)+\varepsilon^p\theta\left(\frac{x_1}{\varepsilon},\frac{x_2}{\varepsilon}\right)\vect{a}_{3}(x_1,x_2)$, where $\theta$ is $[0,1)^2$-periodic function and $p=2$. We also assume that the strain energy of the shell has the Koiter's model.