TY - THES A1 - Nanthakumar, S.S. T1 - Inverse and optimization problems in piezoelectric materials using Extended Finite Element Method and Level sets T1 - Inverse und Optimierungsprobleme für piezoelektrische Materialien mit der Extended Finite Elemente Methode und Level sets N2 - Piezoelectric materials are used in several applications as sensors and actuators where they experience high stress and electric field concentrations as a result of which they may fail due to fracture. Though there are many analytical and experimental works on piezoelectric fracture mechanics. There are very few studies about damage detection, which is an interesting way to prevent the failure of these ceramics. An iterative method to treat the inverse problem of detecting cracks and voids in piezoelectric structures is proposed. Extended finite element method (XFEM) is employed for solving the inverse problem as it allows the use of a single regular mesh for large number of iterations with different flaw geometries. Firstly, minimization of cost function is performed by Multilevel Coordinate Search (MCS) method. The XFEM-MCS methodology is applied to two dimensional electromechanical problems where flaws considered are straight cracks and elliptical voids. Then a numerical method based on combination of classical shape derivative and level set method for front propagation used in structural optimization is utilized to minimize the cost function. The results obtained show that the XFEM-level set methodology is effectively able to determine the number of voids in a piezoelectric structure and its corresponding locations. The XFEM-level set methodology is improved to solve the inverse problem of detecting inclusion interfaces in a piezoelectric structure. The material interfaces are implicitly represented by level sets which are identified by applying regularisation using total variation penalty terms. The formulation is presented for three dimensional structures and inclusions made of different materials are detected by using multiple level sets. The results obtained prove that the iterative procedure proposed can determine the location and approximate shape of material subdomains in the presence of higher noise levels. Piezoelectric nanostructures exhibit size dependent properties because of surface elasticity and surface piezoelectricity. Initially a study to understand the influence of surface elasticity on optimization of nano elastic beams is performed. The boundary of the nano structure is implicitly represented by a level set function, which is considered as the design variable in the optimization process. Two objective functions, minimizing the total potential energy of a nanostructure subjected to a material volume constraint and minimizing the least square error compared to a target displacement, are chosen for the numerical examples. The numerical examples demonstrate the importance of size and aspect ratio in determining how surface effects impact the optimized topology of nanobeams. Finally a conventional cantilever energy harvester with a piezoelectric nano layer is analysed. The presence of surface piezoelectricity in nano beams and nano plates leads to increase in electromechanical coupling coefficient. Topology optimization of these piezoelectric structures in an energy harvesting device to further increase energy conversion using appropriately modified XFEM-level set algorithm is performed . KW - Finite-Elemente-Methode KW - Piezoelectricity KW - Inverse problems KW - Optimization problems KW - Nanostructures KW - XFEM KW - level set method KW - Surface effects Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20161128-27095 ER - TY - THES A1 - Habtemariam, Abinet Kifle T1 - Numerical Demolition Analysis of a Slender Guyed Antenna Mast N2 - The main purpose of the thesis is to ensure the safe demolition of old guyed antenna masts that are located in different parts of Germany. The major problem in demolition of this masts is the falling down of the masts in unexpected direction because of buckling problem. The objective of this thesis is development of a numerical models using finite element method (FEM) and assuring a controlled collapse by coming up with different time setups for the detonation of explosives which are responsible for cutting down the cables. The result of this thesis will avoid unexpected outcomes during the demolition processes and prevent risk of collapsing of the mast over near by structures. KW - Abbruch KW - Finite-Elemente-Methode KW - Optimierung KW - Demolition KW - Guyed antenna masts KW - Explicit finite element method KW - Optimization Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20210723-44609 ER - TY - THES A1 - Zacharias, Christin T1 - Numerical Simulation Models for Thermoelastic Damping Effects N2 - Finite Element Simulations of dynamically excited structures are mainly influenced by the mass, stiffness, and damping properties of the system, as well as external loads. The prediction quality of dynamic simulations of vibration-sensitive components depends significantly on the use of appropriate damping models. Damping phenomena have a decisive influence on the vibration amplitude and the frequencies of the vibrating structure. However, developing realistic damping models is challenging due to the multiple sources that cause energy dissipation, such as material damping, different types of friction, or various interactions with the environment. This thesis focuses on thermoelastic damping, which is the main cause of material damping in homogeneous materials. The effect is caused by temperature changes due to mechanical strains. In vibrating structures, temperature gradients arise in adjacent tension and compression areas. Depending on the vibration frequency, they result in heat flows, leading to increased entropy and the irreversible transformation of mechanical energy into thermal energy. The central objective of this thesis is the development of efficient simulation methods to incorporate thermoelastic damping in finite element analyses based on modal superposition. The thermoelastic loss factor is derived from the structure's mechanical mode shapes and eigenfrequencies. In subsequent analyses that are performed in the time and frequency domain, it is applied as modal damping. Two approaches are developed to determine the thermoelastic loss in thin-walled plate structures, as well as three-dimensional solid structures. The realistic representation of the dissipation effects is verified by comparing the simulation results with experimentally determined data. Therefore, an experimental setup is developed to measure material damping, excluding other sources of energy dissipation. The three-dimensional solid approach is based on the determination of the generated entropy and therefore the generated heat per vibration cycle, which is a measure for thermoelastic loss in relation to the total strain energy. For thin plate structures, the amount of bending energy in a modal deformation is calculated and summarized in the so-called Modal Bending Factor (MBF). The highest amount of thermoelastic loss occurs in the state of pure bending. Therefore, the MBF enables a quantitative classification of the mode shapes concerning the thermoelastic damping potential. The results of the developed simulations are in good agreement with the experimental results and are appropriate to predict thermoelastic loss factors. Both approaches are based on modal superposition with the advantage of a high computational efficiency. Overall, the modeling of thermoelastic damping represents an important component in a comprehensive damping model, which is necessary to perform realistic simulations of vibration processes. N2 - Die Finite-Elemente Simulation von dynamisch angeregten Strukturen wird im Wesentlich durch die Steifigkeits-, Massen- und Dämpfungseigenschaften des Systems sowie durch die äußere Belastung bestimmt. Die Vorhersagequalität von dynamischen Simulationen schwingungsanfälliger Bauteile hängt wesentlich von der Verwendung geeigneter Dämpfungsmodelle ab. Dämpfungsphänomene haben einen wesentlichen Einfluss auf die Schwingungsamplitude, die Frequenz und teilweise sogar die Existenz von Vibrationen. Allerdings ist die Entwicklung von realitätsnahen Dämpfungsmodellen oft schwierig, da eine Vielzahl von physikalischen Effekten zur Energiedissipation während eines Schwingungsvorgangs führt. Beispiele hierfür sind die Materialdämpfung, verschiedene Formen der Reibung sowie vielfältige Wechselwirkungen mit dem umgebenden Medium. Diese Dissertation befasst sich mit thermoelastischer Dämpfung, die in homogenen Materialien die dominante Ursache der Materialdämpfung darstellt. Der thermoelastische Effekt wird ausgelöst durch eine Temperaturänderung aufgrund mechanischer Spannungen. In der schwingenden Struktur entstehen während der Deformation Temperaturgradienten zwischen benachbarten Regionen unter Zug- und Druckbelastung. In Abhängigkeit von der Vibrationsfrequenz führen diese zu Wärmeströmen und irreversibler Umwandlung mechanischer in thermische Energie. Die Zielstellung dieser Arbeit besteht in der Entwicklung recheneffizienter Simulationsmethoden, um thermoelastische Dämpfung in zeitabhängigen Finite-Elemente Analysen, die auf modaler Superposition beruhen, zu integrieren. Der thermoelastische Verlustfaktor wird auf der Grundlage der mechanischen Eigenformen und -frequenzen bestimmt. In nachfolgenden Analysen im Zeit- und Frequenzbereich wird er als modaler Dämpfungsgrad verwendet. Zwei Ansätze werden entwickelt, um den thermoelastischen Verlustfaktor in dünn-wandigen Plattenstrukturen, sowie in dreidimensionalen Volumenbauteilen zu simulieren. Die realitätsnahe Vorhersage der Energiedissipation wird durch die Verifizierung an experimentellen Daten bestätigt. Dafür wird ein Versuchsaufbau entwickelt, der eine Messung von Materialdämpfung unter Ausschluss anderer Dissipationsquellen ermöglicht. Für den Fall der Volumenbauteile wird ein Ansatz verwendet, der auf der Berechnung der Entropieänderung und damit der erzeugte Wärmeenergie während eines Schwingungszyklus beruht. Im Verhältnis zur Formänderungsenergie ist dies ein Maß für die thermoelastische Dämpfung. Für dünne Plattenstrukturen wird der Anteil an Biegeenergie in der Eigenform bestimmt und im sogenannten modalen Biegefaktor (MBF) zusammengefasst. Der maximale Grad an thermoelastischer Dämpfung kann im Zustand reiner Biegung auftreten, sodass der MBF eine quantitative Klassifikation der Eigenformen hinsichtlich ihres thermoelastischen Dämpfungspotentials zulässt. Die Ergebnisse der entwickelten Simulationsmethoden stimmen sehr gut mit den experimentellen Daten überein und sind geeignet, um thermoelastische Dämpfungsgrade vorherzusagen. Beide Ansätze basieren auf modaler Superposition und ermöglichen damit zeitabhängige Simulationen mit einer hohen Recheneffizienz. Insgesamt stellt die Modellierung der thermoelastischen Dämpfung einen Baustein in einem umfassenden Dämpfungsmodell dar, welches zur realitätsnahen Simulation von Schwingungsvorgängen notwendig ist. T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2022,8 KW - Werkstoffdämpfung KW - Finite-Elemente-Methode KW - Strukturdynamik KW - Thermoelastic damping KW - modal damping KW - decay experiments KW - energy dissipation Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20221116-47352 ER -