Kienzler, Reinhold
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Kienzler, Reinhold
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Kienzler, Reinhold
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Item-typ:Veröffentlichung, Bio-inspired load-bearing strategies in engineering design(2025-05-15); 58 69 - Some of the metrics are blocked by yourconsent settings
Item-typ:Veröffentlichung, On the development and mathematical justification of consistent-plate theories of any approximation order(2022-03-21); ; ; Plate theories are widely used to calculate the statics of two-dimensional, thin-walled and plane structures (e.g., ceilings in civil engineering). Classically, the derivation of these theories is based on kinematical a-priori assumptions (cf. Bernoulli assumptions). On the other hand, consistent-plate theories are developed in a mathematically rigorous manner from the generally accepted three-dimensional theory of linear elasticity. This systematic derivation offers many advantages for the development of plate theories for more complex materials. In Schneider & Kienzler (Schneider and Kienzler, 2020), consistent theories are derived for quasi one-dimensional continua. We adopt their argumentation for the development of consistent two-dimensional theories. In doing so, we first arrive from the elastic and dual potential of the three-dimensional theory by means of Taylor-series expansions at the “quasi-two-dimensional problem”. We show that this problem decouples into a plate and a disc problem for certain anisotropy. Moreover, we prove that the coupling relations follow from the sparsity scheme of the stiffness tensor. Using the “consistent-approximation approach”, which estimates the magnitude of the potential parts via powers of a geometric parameter, we finally obtain hierarchical “generic-(consistent) plate theories” . By applying the “pseudo-reduction method”, these systems of partial-differential equations (PDE systems) finally can be reduced to one main PDE, depending only on the main variable, and several reduction PDEs, expressing the non-main variables in dependence of the main variable. Following Kienzler & Schneider (Kienzler and Schneider, 2017), we decompose the variables (coefficients of the Taylor series of the displacements) into their energetic parts. This allows us to prove for the generic-plate theories that the displacement coefficients have a modular structure. Using this modularity, we develop the “complete-(consistent) plate theories”, by which all displacement coefficients can be calculated (proof). Moreover, we present a computer program that automatically generates complete-plate theories of arbitrary approximation orders and that reduces them to a main PDE and several reduction PDEs. It turns out that these PDEs satisfy the PDE systems of the three-dimensional theory. Based on this finding, we derive directly from the three-dimensional theory the “ original-(consistent) plate theories”. Again, we prove that all displacement coefficients can be calculated and develop a program that automatically establishes and reduces original-plate theories of arbitrary approximation orders. A comparison of the complete and original-plate theories reveals that their main and reduction PDEs coincide. Based on this observation, we establish the relations between both theories. Furthermore, we give formulas for some main and reduction PDEs that follow a pattern across all approximation orders and motivate the use of the consistent-approximation approach and modularity from a mathematical point of view. Using the main and reduction PDEs, it is finally proved that the third component of the curl of the displacement field is zero. By means of the Helmholtz decomposition, a comparison of this finding with a finite-element simulation makes it clear that our displacement approach is not complete. On the basis of additional coefficients and by changing one assumption of the consistent-approximation approach, we arrive at the “original-plate theories for the boundary layer”. We prove that all displacement coefficients of these theories can be calculated and give a analytical formula for the main PDEs of arbitrary approximation order. It turns out that the first-order main PDE agrees with the second PDE of Reissner’s plate theory except for a prefactor.Dissertation261 256 - Some of the metrics are blocked by yourconsent settings
Item-typ:Veröffentlichung, Impact of structural components on natural vibrations. How the inspiration by nature can help us improve vibration properties(2021-11-26); ; ; Seit Jahrzehnten wird das Ziel verfolgt, durch ein optimiertes Design Resonanz zu vermeiden, was für viele technische Bereiche – vor allem im Bereich Leichtbau – von großem Interesse ist. Ein Ansatz hierbei ist die Erhöhung (Maximierung) der Struktureigenfrequenzen. In dieser Arbeit wird eine detaillierte Literaturübersicht zu technischen Leichtbaustrukturen und Strukturoptimierung mit Fokus auf Schwingungseigenschaften gegeben. Anschließend untersuchen verschiedene Studien die Anwendung biologisch inspirierter Strukturen und Methoden zur Erhöhung von Eigenfrequenzen. In den Schalen von Diatomeen ist eine Verformung nach den Eigenmoden nachgewiesen worden, was zu der Annahme einer Schwingungsoptimierung in den Schalenstrukturen führt. Inspiriert von dieser Tatsache wird durch eine Vorverformung von Balken (1D) und Platten (2D) nach ihren Eigenmoden eine enorme Eigenfrequenzerhöhung bei konstanter Masse erzielt. Die Ergebnisse werden mit Optimierungen basierend auf der Evolutionsstrategie und – im Fall der Platte – mit Topographieoptimierungen unter Verwendung kommerziell erhältlicher Optimierer verglichen. Im Hinblick auf komplexe Waben- und Gitterstrukturen, die in aquatischen Planktonorganismen zu finden sind, zeigen die durchgeführten Untersuchungen eine starke Erhöhung der ersten Eigenfrequenz mit zunehmender Strukturkomplexität. Als ein technisches Anwendungsbeispiel für bio-inspirierte Schwingungsoptimierung wird ein in der Synchrotronstrahlungsquelle PETRA IV bei DESY eingesetzter Magnetträger untersucht. Eine Parameterstudie analysiert den Einfluss verschiedener Randbedingungen wie veränderliche Lasten, Lagerdefinitionen und Materialeigenschaften auf den Magnetträgeraufbau. Im Anschluss wird ein Entwicklungsprozess für eine Magnetträgerstruktur entwickelt. Basierend auf dem Ergebnis einer Topologieoptimierung lässt sich ein parametrisches Balken-Schalen-Modell erstellen, in das bio-inspirierte Strukturen integriert werden. Die darauffolgende Querschnittsoptimierung unter Verwendung der Evolutionsstrategie führt zu einer optimierten Trägerstruktur. Die Eigenfrequenzmessungen der gegossenen Trägerstruktur erlauben eine Validierung der numerischen Ergebnisse.Dissertation1065 361 - Some of the metrics are blocked by yourconsent settings
Item-typ:Veröffentlichung, Influence of Microstructure on Damage Behavior of Sound Absorbing CeramicsPorous sound-absorbing ceramics contribute to the passive damping of thermo-acoustic instabilities and sound dissipation. As ceramic liners, they must satisfy all requirements respecting mechanical strength and thermal resistance. Design and development of such ceramics concern various aspects like thermal shock resistance, crack behavior, fatigue limit, creep and erosion resistance. The aim of this work is to investigate the mechanical behavior of highly porous sound absorbing ceramics and to predict the brittle damage behavior considering the material microstructure. It studies the applicability of such ceramics as insulation liners for the combustion chambers and gives a clue to further material improvement in terms of mechanical strength. Experiments were performed in this work to characterize the mechanical strengths of a new developed sound absorbing ceramic for the application as ceramic heat shields for the combustion chambers of premixed gas turbines. Compressive tests at both room and high temperature as well as four-point bending tests at room temperature have been carried out. Furthermore, the fits of fracture strengths of the material to the Normal, Weibull and Type I extreme value distributions are investigated. The characterization was then expanded to other physical properties such as porosity, density, thermal conduction coefficients and thermal expansion coefficients. A non-multi-physic but multi-scale approach is applied in this work which predicts the influence of the microstructure on the macroscopic properties. The scale transition method is known as mean-field homogenization method, based on assumed relations between average values of micro-strain and -stress fields in each phase. This homogenization model is based on the Eshelby model and assumes the pores (or rather inclusions) to be ellipsoidal. Influence of the pore density, pore form and pore orientation on the strength of these porous sound absorbing ceramic are studied here. Depending on the loading condition higher strength by higher porosity values is achievable by for example aligning the pores on a desired direction or changing their form from spherical to ellipsoid with high aspect ratios. Furthermore, direct finite element simulations of a representative-volume element (RVE) are also implemented in this work to investigate the pure brittle damage of this sound absorbing ceramic. An effective-stress degradation model has been implemented in a predefined user-subroutine of ABAQUS. It is based on the three dimensional rupture criterion and describes the pure brittle damage under mechanical, thermomechanical, static and quasi-static loadings. Different RVE s have been generated and investigated in terms of damage considering different structural parameters. The present results demonstrate the application potential of these sound absorbing ceramic as liner in terms of mechanical strengths, predict their brittle damage behavior considering the microstructure and provide a base for further material developments and numerical investigations. The applicability of these ceramic to line the combustion chambers in terms of sound absorption is investigated on an experimental set-up at the Faculty of Combustion of the Center of Applied Space Technology and Microgravity (ZARM). The validation of the results from this chapter will be performed on this set-up.Dissertation329 163