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Bibliografie

Conference Paper (international conference)

Numerical minimization of energy functionals in continuum mechanics using hp-FEM in MATLAB

Moskovka Alexej, Frost Miroslav, Valdman Jan

: Computational mechanics 2023. Proceedings of computational mechanics 2023, p. 130-132 , Eds: Adámek V., Jonášová A., Plánička S.

: Computational mechanics 2023 /38./, (Srní, CZ, 20231023)

: GA22-20181S, GA ČR, GF21-06569K, GA ČR

: hp-FEM, energy functionals, numerical minimization

: https://compmech.kme.zcu.cz/download/proceedings/CM2023_Conference_Proceedings.pdf

(eng): 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.

: BC

: 10102