Existence and uniqueness results for a nonlinear Budiansky-Sanders shell model

TL;DR

This paper establishes the existence and uniqueness of solutions for a nonlinear Budiansky-Sanders shell model under certain force conditions, extending previous linear model results to nonlinear cases with broad geometric applicability.

Contribution

It introduces a nonlinear variant of the Budiansky-Sanders shell model and proves existence and uniqueness of solutions under specific assumptions, broadening the model's applicability.

Findings

Existence of a minimizer under certain force conditions

Uniqueness of the minimizer for small applied forces

Applicability to various shell geometries

Abstract

A nonlinear shell model is studied in this paper. This is a nonlinear variant of the Budiansky-Sanders linear shell model. Under some suitable assumptions on the magnitude of the applied force, we will prove the existence of a minimizer for this shell model. In addition, we will also show that our existence result can be applied to all kinds of geometries of the middle surface of the shell. We will also show that the minimizer found in this fashion is unique, provided the applied forces are small enough. Our result hence extends the one given by Destuynder in [1].