Fractional-Order Shell Theory: Formulation and Application to the Analysis of Nonlocal Cylindrical Panels

TL;DR

This paper develops a fractional calculus-based framework for analyzing the nonlocal static response of cylindrical shell panels, enabling accurate modeling of long-range interactions in curved structures using an extended finite element method.

Contribution

It introduces a novel fractional-order shell theory with a computational approach for nonlocal analysis of cylindrical shells, incorporating nonlinear effects and practical boundary conditions.

Findings

Effective modeling of nonlocal elastic interactions in shells

Accurate prediction of linear and nonlinear static responses

Extension of fractional-Finite Element Method to shell structures

Abstract

We present a theoretical and computational framework based on fractional calculus for the analysis of the nonlocal static response of cylindrical shell panels. The differ-integral nature of fractional derivatives allows an efficient and accurate methodology to account for the effect of long-range (nonlocal) interactions in curved structures. More specifically, the use of frame-invariant fractional-order kinematic relations enables a physically, mathematically, and thermodynamically consistent formulation to model the nonlocal elastic interactions. In order to evaluate the response of these nonlocal shells under practical scenarios involving generalized loads and boundary conditions, the fractional-Finite Element Method (f-FEM) is extended to incorporate shell elements based on the first-order shear-deformable displacement theory. Finally, numerical studies are performed exploring both the linear and the geometrically nonlinear static response of nonlocal cylindrical shell panels. This study is intended to provide a general foundation to investigate the nonlocal behavior of curved structures by means of fractional order models.