Asymptotic behavior of a nonlinear shallow shell model when the shell becomes a plate

TL;DR

This paper investigates the asymptotic behavior of solutions in a nonlinear shallow shell model as the shell approaches a plate, extending previous results to more general applied forces.

Contribution

It provides a comprehensive analysis of the asymptotic behavior of the model's solutions, including cases with non-vanishing tangential forces, broadening previous findings.

Findings

Asymptotic behavior characterized for general applied forces

Extension of previous results to non-vanishing tangential forces

Provides theoretical insights into shell-to-plate transition

Abstract

This paper studies a nonlinear shallow shell model proposed by Donnell, Vlasov, Mushtari, Galimov, and Koiter. More specifically, we address the question concerning the asymptotic behavior of minimizing solutions. Our result can be applied to general applied forces. Thus, it substantially extends the one given in \cite{oana2} whereby the tangential components of the applied forces are assumed to vanish.