A gradient based numerical approach to simulate elastic rod

Abdul Majid

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 190, issue C, 1048-1055

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.

Keywords: Bending energy; Twist energy; Inextensibility; Conjugate gradient; Preconditioning (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:190:y:2021:i:c:p:1048-1055

DOI: 10.1016/j.matcom.2021.07.001

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