Existence theorems in the geometrically non-linear 6-parametric theory of elastic plates

TL;DR

This paper proves the existence of solutions for the complex non-linear equations governing elastic plates within a 6-parametric shell theory, covering both isotropic and anisotropic cases, and compares with Cosserat models.

Contribution

It establishes the first existence theorems for global minimizers in the geometrically exact 6-parametric shell theory for elastic plates.

Findings

Existence of global minimizers for isotropic plates.

Extension of existence results to anisotropic plates.

Comparison with Cosserat plate models.

Abstract

In this paper we show the existence of global minimizers for the geometrically exact, non-linear equations of elastic plates, in the framework of the general 6-parametric shell theory. A characteristic feature of this model for shells is the appearance of two independent kinematic fields: the translation vector field and the rotation tensor field (representing in total 6 independent scalar kinematic variables). For isotropic plates, we prove the existence theorem by applying the direct methods of the calculus of variations. Then, we generalize our existence result to the case of anisotropic plates. We also present a detailed comparison with a previously established Cosserat plate model.