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Networks of Nonlinear Thin Structures - Theory and Applications
Christoph Strohmeyer
2018
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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.
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Keywords
- adjoint equation
- Adjungierte Differentialgleichung
- Adjungierte Gleichung
- Balkentheorie
- beam theory
- boundary controllability
- boundary observability
- Control theory
- creep damage
- Druckrohrleitung
- effective mechanical properties
- Effektive Materialeigenschaften
- energetic homogenization
- Energetische Homogenisierung
- Geometisch exakter Balken
- geometrically exact beam
- Geometrieoptimierung
- geometry optimization
- hyperbolic systems
- Hyperbolische Systeme
- Kontrolltheorie
- Kriechschädigung
- mathematische Modellierung
- modeling
- Modellierung
- nichtlineare Kontrolltheorie
- non-woven
- Numerics
- Numerik
- Optimal Control
- Optimalsteuerung
- piping system
- Randbeobachtbarkeit
- Randsteuerbarkeit
- Rohrleitungssystem
- Schadensmechanik
- Sensitivitätsanalyse
- sensitivity analysis
- Software Engineering Programmtransformation
- Steuerbarkeit
- Strukturoptimierung
- Textilfaser
- thema EDItEUR::P Mathematics and Science
- Vorverformter Balken
- Wirrvlies
Links
DOI: 10.25593/978-3-96147-138-6Editions