Original title: Numerical minimization of energy functionals in continuum mechanics using hp-FEM in MATLAB
Authors: Moskovka, Alexej ; Frost, Miroslav ; Valdman, Jan
Document type: Papers
Conference/Event: Computational mechanics 2023 /38./, Srní (CZ), 20231023
Year: 2023
Language: eng
Abstract: Many processes in mechanics and thermodynamics can be formulated as a minimization of a particular energy functional. The finite element method can be used for an approximation of such functionals in a finite-dimensional subspace. Consequently, the numerical minimization methods (such as quasi-Newton and trust region) can be used to find a minimum of the functional. Vectorization techniques used for the evaluation of the energy together with the assembly of discrete energy gradient and Hessian sparsity are crucial for evaluation times. A particular model simulating the deformation of a Neo-Hookean solid body is solved in this contribution by minimizing the corresponding energy functional. We implement both P1 and rectangular hp-finite elements and compare their efficiency with respect to degrees of freedom and evaluation times.
Keywords: energy functionals; hp-FEM; numerical minimization
Project no.: GA22-20181S (CEP), GF21-06569K (CEP)
Funding provider: GA ČR, GA ČR
Host item entry: Computational mechanics 2023. Proceedings of computational mechanics 2023, ISBN 978-80-261-1177-1

Institution: Institute of Thermomechanics AS ČR (web)
Document availability information: Fulltext is available at external website.
External URL: https://compmech.kme.zcu.cz/download/proceedings/CM2023_Conference_Proceedings.pdf
Original record: https://hdl.handle.net/11104/0349460

Permalink: http://www.nusl.cz/ntk/nusl-538542


The record appears in these collections:
Research > Institutes ASCR > Institute of Thermomechanics
Conference materials > Papers