Networks of Nonlinear Thin Structures - Theory and Applications
This thesis is concerned with modeling, analysis and applications of one-dimensional continua and networks thereof. More precisely, we use the pre-curved and -twisted three-dimensional geometrically exact beam theory to rigorously deduce several well-known models: the pre-curved two-dimensional geo...
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| Fformat: | Online |
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FAU University Press
2025
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| Mynediad Ar-lein: | ONIX_20251215T160703_9783961471386_23 |
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| _version_ | 1869531560260141056 |
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| author | Strohmeyer, Christoph |
| author_browse | Strohmeyer, Christoph |
| author_facet | Strohmeyer, Christoph |
| author_sort | Strohmeyer, Christoph |
| collection | Directory of Open Access Books |
| description | This thesis is concerned with modeling, analysis and applications of one-dimensional continua and networks thereof. More precisely, we use the pre-curved and -twisted three-dimensional geometrically exact beam theory to rigorously deduce several well-known models: the pre-curved two-dimensional geometrically exact beam, the pre-curved and -twisted three-dimensional linear Timoshenko beam, as weil as the geometrically nonlinear truss and string. Based on the abstract theory of first-order quasilinear hyperbolic systems, we show in the second part of this thesis local exact boundary controllability and observability for the second-order system of pre-curved two-dimensional geometrically exact beams. Additionally, we formulate an optimal control problem for this system, derive the adjoint equation and identify conditions, that allow for classical adjoint states. The one-dimensional models given in this thesis are used in different applications. First, we develop a numerical scheme that solves the optimal control problem for two-dimensional geometrically exact beams. Subsequently, we employ the concept of energetic homogenization to determine effective material properties of a Kirchhoff-Love plate from networks of linear Timoshenko beams and optimize their geometry. With a similar idea, applied at two levels, non-periodic networks of nonlinear strings are homogenized in order to match the behavior of non-woven fiber mats. Finally, the damaging of high-pressure pipes is investigated, which requires a nonlinear path-dependent material law coupled to the three-dimensional geometrically exact beam. In this scenario a creep-damage material law is modeled, numerically implemented and its feasibility to describe piping systems demonstrated. |
| format | Online |
| id | doab-20.500.12854ir-170258 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| publisher | FAU University Press |
| publisherStr | FAU University Press |
| record_format | ojs |
| spelling | doab-20.500.12854ir-1702582025-12-16T05:39:33Z Networks of Nonlinear Thin Structures - Theory and Applications Strohmeyer, Christoph Mathematische Modellierung Randbeobachtbarkeit Steuerbarkeit Schadensmechanik Balkentheorie Hyperbolische Systeme creep damage Energetische Homogenisierung Geometisch exakter Balken effective mechanical properties non-woven beam theory Textilfaser sensitivity analysis Geometrieoptimierung Wirrvlies Optimalsteuerung geometrically exact beam boundary observability modeling Adjungierte Differentialgleichung optimal control Adjungierte Gleichung Software Engineering Programmtransformation Vorverformter Balken boundary controllability control theory Kontrolltheorie Strukturoptimierung Numerik nichtlineare Kontrolltheorie geometry optimization piping system Druckrohrleitung adjoint equation Sensitivitätsanalyse Randsteuerbarkeit Kriechschädigung Modellierung Effektive Materialeigenschaften Rohrleitungssystem energetic homogenization hyperbolic systems numerics thema EDItEUR::P Mathematics and Science This thesis is concerned with modeling, analysis and applications of one-dimensional continua and networks thereof. More precisely, we use the pre-curved and -twisted three-dimensional geometrically exact beam theory to rigorously deduce several well-known models: the pre-curved two-dimensional geometrically exact beam, the pre-curved and -twisted three-dimensional linear Timoshenko beam, as weil as the geometrically nonlinear truss and string. Based on the abstract theory of first-order quasilinear hyperbolic systems, we show in the second part of this thesis local exact boundary controllability and observability for the second-order system of pre-curved two-dimensional geometrically exact beams. Additionally, we formulate an optimal control problem for this system, derive the adjoint equation and identify conditions, that allow for classical adjoint states. The one-dimensional models given in this thesis are used in different applications. First, we develop a numerical scheme that solves the optimal control problem for two-dimensional geometrically exact beams. Subsequently, we employ the concept of energetic homogenization to determine effective material properties of a Kirchhoff-Love plate from networks of linear Timoshenko beams and optimize their geometry. With a similar idea, applied at two levels, non-periodic networks of nonlinear strings are homogenized in order to match the behavior of non-woven fiber mats. Finally, the damaging of high-pressure pipes is investigated, which requires a nonlinear path-dependent material law coupled to the three-dimensional geometrically exact beam. In this scenario a creep-damage material law is modeled, numerically implemented and its feasibility to describe piping systems demonstrated. 2025-12-16T05:39:32Z 2025-12-16T05:39:32Z 2025-12-15T15:09:45Z 2018 book ONIX_20251215T160703_9783961471386_23 https://library.oapen.org/handle/20.500.12657/109192 9783961471386 9783961471379 https://directory.doabooks.org/handle/20.500.12854/170258 eng FAU Studies Mathematics & Physics open access image/jpeg Attribution 4.0 International https://library.oapen.org/bitstream/20.500.12657/109192/1/9783961471386.pdf FAU University Press 10.25593/978-3-96147-138-6 10.25593/978-3-96147-138-6 2c600dea-eece-4066-87be-da335e323fdb 9783961471386 9783961471379 283 Erlangen open access |
| spellingShingle | Mathematische Modellierung Randbeobachtbarkeit Steuerbarkeit Schadensmechanik Balkentheorie Hyperbolische Systeme creep damage Energetische Homogenisierung Geometisch exakter Balken effective mechanical properties non-woven beam theory Textilfaser sensitivity analysis Geometrieoptimierung Wirrvlies Optimalsteuerung geometrically exact beam boundary observability modeling Adjungierte Differentialgleichung optimal control Adjungierte Gleichung Software Engineering Programmtransformation Vorverformter Balken boundary controllability control theory Kontrolltheorie Strukturoptimierung Numerik nichtlineare Kontrolltheorie geometry optimization piping system Druckrohrleitung adjoint equation Sensitivitätsanalyse Randsteuerbarkeit Kriechschädigung Modellierung Effektive Materialeigenschaften Rohrleitungssystem energetic homogenization hyperbolic systems numerics thema EDItEUR::P Mathematics and Science Strohmeyer, Christoph Networks of Nonlinear Thin Structures - Theory and Applications |
| title | Networks of Nonlinear Thin Structures - Theory and Applications |
| title_full | Networks of Nonlinear Thin Structures - Theory and Applications |
| title_fullStr | Networks of Nonlinear Thin Structures - Theory and Applications |
| title_full_unstemmed | Networks of Nonlinear Thin Structures - Theory and Applications |
| title_short | Networks of Nonlinear Thin Structures - Theory and Applications |
| title_sort | networks of nonlinear thin structures theory and applications |
| topic | Mathematische Modellierung Randbeobachtbarkeit Steuerbarkeit Schadensmechanik Balkentheorie Hyperbolische Systeme creep damage Energetische Homogenisierung Geometisch exakter Balken effective mechanical properties non-woven beam theory Textilfaser sensitivity analysis Geometrieoptimierung Wirrvlies Optimalsteuerung geometrically exact beam boundary observability modeling Adjungierte Differentialgleichung optimal control Adjungierte Gleichung Software Engineering Programmtransformation Vorverformter Balken boundary controllability control theory Kontrolltheorie Strukturoptimierung Numerik nichtlineare Kontrolltheorie geometry optimization piping system Druckrohrleitung adjoint equation Sensitivitätsanalyse Randsteuerbarkeit Kriechschädigung Modellierung Effektive Materialeigenschaften Rohrleitungssystem energetic homogenization hyperbolic systems numerics thema EDItEUR::P Mathematics and Science |
| topic_facet | Mathematische Modellierung Randbeobachtbarkeit Steuerbarkeit Schadensmechanik Balkentheorie Hyperbolische Systeme creep damage Energetische Homogenisierung Geometisch exakter Balken effective mechanical properties non-woven beam theory Textilfaser sensitivity analysis Geometrieoptimierung Wirrvlies Optimalsteuerung geometrically exact beam boundary observability modeling Adjungierte Differentialgleichung optimal control Adjungierte Gleichung Software Engineering Programmtransformation Vorverformter Balken boundary controllability control theory Kontrolltheorie Strukturoptimierung Numerik nichtlineare Kontrolltheorie geometry optimization piping system Druckrohrleitung adjoint equation Sensitivitätsanalyse Randsteuerbarkeit Kriechschädigung Modellierung Effektive Materialeigenschaften Rohrleitungssystem energetic homogenization hyperbolic systems numerics thema EDItEUR::P Mathematics and Science |
| url | ONIX_20251215T160703_9783961471386_23 |
| work_keys_str_mv | AT strohmeyerchristoph networksofnonlinearthinstructurestheoryandapplications |