A Comprehensive Comparative Study on the Nonlinear Finite Element and Isogeometric Analyses of Shell-Type Structures

Abstract

This article presents a comparative study of the computational characteristics of Finite Element Analysis (FEA) and Isogeometric Analysis (IGA) in studying large elastic deformations and large-amplitude vibrations of shell-type structures. A geometrically nonlinear seven-parameter shell model is employed in a Lagrangian description in which the shell deformation is represented in mid-surface. Using a curvilinear coordinate system suitable for various geometries, the kinematic and kinetic of the problem are established, and Hamilton's principle is applied to derive the governing equations. The strain–displacement relationships and consequently, the remaining variational formulations are expressed in a matrix-vector form, allowing for direct implementation in both FEA and IGA. This efficient formulation enables a fair and consistent comparison between the two methods. Several numerical examples are examined, including the well-known static benchmark problems and their corresponding forced vibration analyses. The primary contribution of this article is the demonstration of the computational efficiency of isogeometric analysis in challenging case studies of geometrically nonlinear shells. Additional novel contributions include deriving a unified formulation for seven-parameter FEA and IGA shell models as well as analyzing the large-amplitude free and forced vibrations of shells. © 2025 John Wiley & Sons Ltd.