Datum
2019Schlagwort
620 Ingenieurwissenschaften 690 Hausbau, Bauhandwerk ViskoplastizitätElastoplastische DeformationZeitintegrationsverfahrenGalerkin-MethodeRunge-Kutta-VerfahrenFinite-Elemente-MethodeMehrfeldproblemBenchmarkFehlerabschätzungMetadata
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Buch
Consistent Higher Order Accurate Time Discretization Methods for Inelastic Material Models
Zusammenfassung
The present thesis investigates the usage of higher order accurate time integrators together with appropriate error estimators for small and finite dynamic (visco)plasticity. Therefore, a general (visco)plastic problem is defined which serves as a basis to create closed-form solution strategies. A classical access towards small and finite (visco)plasticity is integrated into this concept. This approach is based on the idea, that the balance of linear momentum is formulated in a weak sense and the material laws are included indirectly. Thus, separate time discretizations are implemented and an appropriate coupling between them is necessary. Limitations for the usage of time integrators are the consequence. In contrast, an alternative multifield formulation is derived, adapting the principle of Jourdain. The idea is to assume that the balance of energy - taking into account a pseudopotential representing dissipative effects – resembles a rate-type functional, whose stationarity condition leads to the equations describing small or finite dynamic (visco)plasticity. Accordingly, the material laws and the balance of linear momentum can be solved on the same level and only one single time discretization has to be performed. A greater freedom in the choice of time integrators is obtained and the application of higher order accurate schemes - such as Newmark’s method, fully implicit as well as diagonally implicit Runge-Kutta schemes, and continuous as well as discontinuous Galerkin methods - is facilitated. An analysis and a comparison of the classical and the multifield formulation is accomplished by means of distinct examples. In this context, a dynamic benchmark problem is developed, which allows to focus on the effect of different time integrators. For this investigation, a variety of time discretization error estimators are formulated, evaluated, and compared.
Zusätzliche Informationen
Zugleich: Dissertation, Universität Kassel, 2019Druckausgabe
Link zu kassel university pressZitieren
@book{doi:10.17170/kobra-202007291513,
author={Schröder, Bettina Anna Barbara},
title={Consistent Higher Order Accurate Time Discretization Methods for Inelastic Material Models},
publisher={kassel university press},
year={2019}
}
0500 Oax 0501 Text $btxt$2rdacontent 0502 Computermedien $bc$2rdacarrier 1100 2019$n2019 1500 1/eng 2050 ##0##http://hdl.handle.net/123456789/11676 3000 Schröder, Bettina Anna Barbara 4000 Consistent Higher Order Accurate Time Discretization Methods for Inelastic Material Models / Schröder, Bettina Anna Barbara 4030 4060 Online-Ressource 4085 ##0##=u http://nbn-resolving.de/http://hdl.handle.net/123456789/11676=x R 4204 \$dBuch 4170 Schriftenreihe Institut für Baustatik und Baudynamik ;; 2019 - 2 5550 {{Viskoplastizität}} 5550 {{Elastoplastische Deformation}} 5550 {{Zeitintegrationsverfahren}} 5550 {{Galerkin-Methode}} 5550 {{Runge-Kutta-Verfahren}} 5550 {{Finite-Elemente-Methode}} 5550 {{Mehrfeldproblem}} 5550 {{Benchmark}} 5550 {{Fehlerabschätzung}} 7136 ##0##http://hdl.handle.net/123456789/11676
2020-08-07T14:30:30Z 2020-08-07T14:30:30Z 2019 doi:10.17170/kobra-202007291513 978-3-7376-0773-5 (e-book) http://hdl.handle.net/123456789/11676 Zugleich: Dissertation, Universität Kassel, 2019 eng kassel university press urn:nbn:de:0002-407733 Namensnennung - Weitergabe unter gleichen Bedingungen 4.0 International http://creativecommons.org/licenses/by-sa/4.0/ 620 690 Consistent Higher Order Accurate Time Discretization Methods for Inelastic Material Models Buch The present thesis investigates the usage of higher order accurate time integrators together with appropriate error estimators for small and finite dynamic (visco)plasticity. Therefore, a general (visco)plastic problem is defined which serves as a basis to create closed-form solution strategies. A classical access towards small and finite (visco)plasticity is integrated into this concept. This approach is based on the idea, that the balance of linear momentum is formulated in a weak sense and the material laws are included indirectly. Thus, separate time discretizations are implemented and an appropriate coupling between them is necessary. Limitations for the usage of time integrators are the consequence. In contrast, an alternative multifield formulation is derived, adapting the principle of Jourdain. The idea is to assume that the balance of energy - taking into account a pseudopotential representing dissipative effects – resembles a rate-type functional, whose stationarity condition leads to the equations describing small or finite dynamic (visco)plasticity. Accordingly, the material laws and the balance of linear momentum can be solved on the same level and only one single time discretization has to be performed. A greater freedom in the choice of time integrators is obtained and the application of higher order accurate schemes - such as Newmark’s method, fully implicit as well as diagonally implicit Runge-Kutta schemes, and continuous as well as discontinuous Galerkin methods - is facilitated. An analysis and a comparison of the classical and the multifield formulation is accomplished by means of distinct examples. In this context, a dynamic benchmark problem is developed, which allows to focus on the effect of different time integrators. For this investigation, a variety of time discretization error estimators are formulated, evaluated, and compared. open access Schröder, Bettina Anna Barbara 2019-05-15 xxx, 31-255 Seiten Schriftenreihe Institut für Baustatik und Baudynamik ;; 2019 - 2 Kassel, Universität Kassel, Fachbereich Bauingenieurwesen und Umweltingenieurwesen Kuhl, Detlef (Prof. Dr.) Schröder, Jörg (Prof. Dr.) Kassel 978-3-7376-0772-8 (print) Viskoplastizität Elastoplastische Deformation Zeitintegrationsverfahren Galerkin-Methode Runge-Kutta-Verfahren Finite-Elemente-Methode Mehrfeldproblem Benchmark Fehlerabschätzung publishedVersion Schriftenreihe Institut für Baustatik und Baudynamik 2019 - 2 true 39,00 Schriftenreihe Institut für Baustatik und Baudynamik Naturwissenschaft, Technik, Informatik, Medizin Dissertation FB 14 / Bauingenieur- und Umweltingenieurwesen
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