materials Article Stability Loss Analysis for Thin-Walled Shells with Elliptical Cross-Sectional Area Ján Kostka 1 , Jozef Bocko 1 , Peter Frankovský 1, * , Ingrid Delyová 1 , Tomáš Kula 1 and Patrik Varga 2   Citation: Kostka, J.; Bocko, J.; Frankovský, P.; Delyová, I.; Kula, T.; Varga, P. Stability Loss Analysis for Thin-Walled Shells with Elliptical Cross-Sectional Area. Materials 2021, 14, 5636. https://doi.org/10.3390/ ma14195636 Academic Editor: Adam Grajcar Received: 14 June 2021 Accepted: 23 September 2021 Published: 28 September 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Department of Applied Mechanics and Mechanical Engineering, Faculty of Mechanical Engineering, Technical University of Košice, 042 00 Košice, Slovakia; jan.kostka@tuke.sk (J.K.); jozef.bocko@tuke.sk (J.B.); ingrid.delyova@tuke.sk (I.D.); tomas.kula@tuke.sk (T.K.) 2 Department of Biomedical Engineering and Measurement, Faculty of Mechanical Engineering, Technical University of Košice, 042 00 Košice, Slovakia; patrik.varga@tuke.sk * Correspondence: peter.frankovsky@tuke.sk Abstract: The aim of the scientific contribution is to point out the possibility of applicability of cylindrical shells with a constant elliptical cross-sectional shape for stability loss analysis. The solution to the problem consists of two approaches. The first approach is the experimental measurement of critical force levels, where the work also describes the method of production of the sample and jigs that cause the desired elliptical shape. The second approach is solving the problem in the use of numerical methods—the finite strip method together with the finite element method. Keywords: thin-walled shells; stability loss; tensile test; FEM 1. Introduction In the introduction, it should be emphasized that the problem of loss of stability for thin-walled shells with an elliptical cross-sectional area has gradually evolved over the past and present centuries. With the advent of more innovative experimental and numerical methods, more accurate results can be achieved. Below, in the article in the historical and current overview of the development of the loss of stability survey, the researched issue is described with individual gradual solutions. One of the first works that dealt with the issue of shell elements with elliptical cross- section is a work published by the author Brown in 1936 [1]. His work describes and conducts the dependencies between stress and strain for shell elements with an elliptical cross-section, which are subjected to internal compressive loads. During this period, many scientists and researchers have focused their attention primarily on shells with a circular cross-section. The obvious reason for this is that structural elements of this type occur very frequently. The rapid development of society, which occurred in the late 40s of the 20th century, brought many problems, especially in the field of aviation. One of the unexplored areas of aviation was the increase in the speed of aircraft, which approached the speed of sound or overcoming it. A serious problem that occurred was the effect of compressive stress on the leading edges of the fighter wings. This type of problem connected with the nose of the wing, whose stability is affected by the changing curvature of the shell, was solved by Marguerre in 1951 [2]. In the study [3], the authors present the derived knowledge for the solution of cylin- drical shells using the energy method for the problem of oval or elliptical cylindrical shells. The authors consider precisely defined geometric dimensions of the elliptical cross-section of the shell and defined boundary conditions. Another important contribution for the given issue of elliptical shells was published by the same authors in [4]. This contribution is mainly based on a dissertation thesis by Chen published in 1964 [5]. In a subsequent paper [6], the authors describe energy expressions and related differential equations for Materials 2021, 14, 5636. https://doi.org/10.3390/ma14195636 https://www.mdpi.com/journal/materials