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

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. 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.

Document Details

Document Type
Pub Defense Publication
Publication Date
Jun 16, 2022
Source ID
10.1115/1.4054677

Entities

People

  • Fabio Semperlotti
  • Sai Sidhardh
  • Sansit Patnaik

Organizations

  • Defense Advanced Research Projects Agency
  • National Science Foundation
  • Purdue University

Tags

Fields of Study

  • Physics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Quantum Chemistry