Linear constrained Cosserat-shell models including terms up to ${O}(h^5)$. Conditional and unconditional existence and uniqueness

TL;DR

This paper linearizes a nonlinear Cosserat-shell model up to order ${O}(h^5)$, compares it with classical shell models, and proves existence and uniqueness of solutions using Korn's inequality.

Contribution

It introduces a linear constrained Cosserat-shell model including higher-order terms and establishes mathematical well-posedness results.

Findings

Comparison with classical shell models clarifies differences and similarities.

Existence and uniqueness are proven for all proposed linear models.

Higher-order terms up to ${O}(h^5)$ are included in the linearization.

Abstract

In this paper we linearise the recently introduced geometrically nonlinear constrained Cosserat-shell model. In the framework of the linear constrained Cosserat-shell model, we provide a comparison of our linear models with the classical linear Koiter shell model and the "best" first order shell model. For all proposed linear models we show existence and uniqueness based on a Korn's inequality for surfaces.