Global existence results and duality for non-linear models of plates and shells

TL;DR

This paper establishes global existence results and duality principles for non-linear models of plates and shells, providing new mathematical insights into their variational formulations and optimality conditions.

Contribution

It introduces a novel proof for the global existence of minimizers and duality principles for Kirchhoff-Love plates and non-linear shell models.

Findings

Proved global existence of minimizers for the Kirchhoff-Love plate model

Developed duality principles and optimality conditions for plate and shell models

Extended results to non-linear shell models with existence and duality frameworks

Abstract

In this article firstly we develop a new proof for global existence of minimizers for the Kirchhoff-Love plate model. We also present a duality principle and relating sufficient optimality conditions for such a variational plate model. In a second step, we present a global existence result for a non-linear model of shells. For this model, we also develop a duality principle and concerning sufficient conditions of optimality.