A gradient based numerical approach to simulate elastic rod

Author Affiliation

Abdul Majid is Assistant Professor at Institute of Business Administration (IBA), Karachi

Faculty / School

School of Mathematics and Computer Science (SMCS)

Department

Department of Mathematical Sciences

Was this content written or created while at IBA?

Yes

Document Type

Article

Source Publication

Mathematics and Computers in Simulation

ISSN

0378-4754

Disciplines

Computer Sciences | Mathematics

Abstract

An efficient numerical method based on a Sobolev gradient is presented to find the equilibrium shapes of an elastic rod resistant to bending and twisting. A Sobolev preconditioning operator is introduced based on the energy of the elastic rod that preconditions the standard conjugate gradient method and results in a speedy convergence. It outperforms the usual conjugate gradient and steepest descent methods without requiring expensive calculation of the dense Hessian associated with the total energy of the rod. The method has also been validated to predict the Michell's instability in a closed rod with a twist.

Indexing Information

HJRS - W Category, Scopus, Web of Science - Science Citation Index Expanded (SCI)

Journal Quality Ranking

Impact Factor: 2.463

Publication Status

Published

Link to Full Text

Share

COinS