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Numerical minimization of energy functionals in continuum mechanics using hp-FEM in MATLAB
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SYSNO ASEP 0579519 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title Numerical minimization of energy functionals in continuum mechanics using hp-FEM in MATLAB Author(s) Moskovka, Alexej (UTIA-B)
Frost, Miroslav (UT-L) RID, ORCID
Valdman, Jan (UTIA-B) RID, ORCIDNumber of authors 3 Source Title Computational mechanics 2023. Proceedings of computational mechanics 2023. - Plzeň : University of West Bohemia, 2023 / Adámek V. ; Jonášová A. ; Plánička S. - ISBN 978-80-261-1177-1 Pages s. 130-132 Number of pages 3 s. Publication form Online - E Action Computational mechanics 2023 /38./ Event date 23.10.2023 - 25.10.2023 VEvent location Srní Country CZ - Czech Republic Event type EUR Language eng - English Country CZ - Czech Republic Keywords hp-FEM ; energy functionals ; numerical minimization Subject RIV BC - Control Systems Theory OECD category Applied mathematics Subject RIV - cooperation Institute of Information Theory and Automation - General Mathematics R&D Projects GA22-20181S GA ČR - Czech Science Foundation (CSF) GF21-06569K GA ČR - Czech Science Foundation (CSF) Institutional support UT-L - RVO:61388998 ; UTIA-B - RVO:67985556 Annotation 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. Workplace Institute of Thermomechanics Contact Marie Kajprová, kajprova@it.cas.cz, Tel.: 266 053 154 ; Jana Lahovská, jaja@it.cas.cz, Tel.: 266 053 823 Year of Publishing 2024
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