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- Finite-Elemente-Methode (4)
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Year of publication
- 2022 (37) (remove)
The Finite Element Method (FEM) is widely used in engineering for solving Partial Differential Equations (PDEs) over complex geometries. To this end, it is required to provide the FEM software with a geometric model that is typically constructed in a Computer-Aided Design (CAD) software. However, FEM and CAD use different approaches for the mathematical description of the geometry. Thus, it is required to generate a mesh, which is suitable for FEM, based on the CAD model. Nonetheless, this procedure is not a trivial task and it can be time consuming. This issue becomes more significant for solving shape and topology optimization problems, which consist in evolving the geometry iteratively. Therefore, the computational cost associated to the mesh generation process is increased exponentially for this type of applications.
The main goal of this work is to investigate the integration of CAD and CAE in shape and topology optimization. To this end, numerical tools that close the gap between design and analysis are presented. The specific objectives of this work are listed below:
• Automatize the sensitivity analysis in an isogeometric framework for applications in shape optimization. Applications for linear elasticity are considered.
• A methodology is developed for providing a direct link between the CAD model and the analysis mesh. In consequence, the sensitivity analysis can be performed in terms of the design variables located in the design model.
• The last objective is to develop an isogeometric method for shape and topological optimization. This method should take advantage of using Non-Uniform Rational B-Splines (NURBS) with higher continuity as basis functions.
Isogeometric Analysis (IGA) is a framework designed to integrate the design and analysis in engineering problems. The fundamental idea of IGA is to use the same basis functions for modeling the geometry, usually NURBS, for the approximation of the solution fields. The advantage of integrating design and analysis is two-fold. First, the analysis stage is more accurate since the system of PDEs is not solved using an approximated geometry, but the exact CAD model. Moreover, providing a direct link between the design and analysis discretizations makes possible the implementation of efficient sensitivity analysis methods. Second, the computational time is significantly reduced because the mesh generation process can be avoided.
Sensitivity analysis is essential for solving optimization problems when gradient-based optimization algorithms are employed. Automatic differentiation can compute exact gradients, automatically by tracking the algebraic operations performed on the design variables. For the automation of the sensitivity analysis, an isogeometric framework is used. Here, the analysis mesh is obtained after carrying out successive refinements, while retaining the coarse geometry for the domain design. An automatic differentiation (AD) toolbox is used to perform the sensitivity analysis. The AD toolbox takes the code for computing the objective and constraint functions as input. Then, using a source code transformation approach, it outputs a code for computing the objective and constraint functions, and their sensitivities as well. The sensitivities obtained from the sensitivity propagation method are compared with analytical sensitivities, which are computed using a full isogeometric approach.
The computational efficiency of AD is comparable to that of analytical sensitivities. However, the memory requirements are larger for AD. Therefore, AD is preferable if the memory requirements are satisfied. Automatic sensitivity analysis demonstrates its practicality since it simplifies the work of engineers and designers.
Complex geometries with sharp edges and/or holes cannot easily be described with NURBS. One solution is the use of unstructured meshes. Simplex-elements (triangles and tetrahedra for two and three dimensions respectively) are particularly useful since they can automatically parameterize a wide variety of domains. In this regard, unstructured Bézier elements, commonly used in CAD, can be employed for the exact modelling of CAD boundary representations. In two dimensions, the domain enclosed by NURBS curves is parameterized with Bézier triangles. To describe exactly the boundary of a two-dimensional CAD model, the continuity of a NURBS boundary representation is reduced to C^0. Then, the control points are used to generate a triangulation such that the boundary of the domain is identical to the initial CAD boundary representation. Thus, a direct link between the design and analysis discretizations is provided and the sensitivities can be propagated to the design domain.
In three dimensions, the initial CAD boundary representation is given as a collection of NURBS surfaces that enclose a volume. Using a mesh generator (Gmsh), a tetrahedral mesh is obtained. The original surface is reconstructed by modifying the location of the control points of the tetrahedral mesh using Bézier tetrahedral elements and a point inversion algorithm. This method offers the possibility of computing the sensitivity analysis using the analysis mesh. Then, the sensitivities can be propagated into the design discretization. To reuse the mesh originally generated, a moving Bézier tetrahedral mesh approach was implemented.
A gradient-based optimization algorithm is employed together with a sensitivity propagation procedure for the shape optimization cases. The proposed shape optimization approaches are used to solve some standard benchmark problems in structural mechanics. The results obtained show that the proposed approach can compute accurate gradients and evolve the geometry towards optimal solutions. In three dimensions, the moving mesh approach results in faster convergence in terms of computational time and avoids remeshing at each optimization step.
For considering topological changes in a CAD-based framework, an isogeometric phase-field based shape and topology optimization is developed. In this case, the diffuse interface of a phase-field variable over a design domain implicitly describes the boundaries of the geometry. The design variables are the local values of the phase-field variable. The descent direction to minimize the objective function is found by using the sensitivities of the objective function with respect to the design variables. The evolution of the phase-field is determined by solving the time dependent Allen-Cahn equation.
Especially for topology optimization problems that require C^1 continuity, such as for flexoelectric structures, the isogeometric phase field method is of great advantage. NURBS can achieve the desired continuity more efficiently than the traditional employed functions. The robustness of the method is demonstrated when applied to different geometries, boundary conditions, and material configurations. The applications illustrate that compared to piezoelectricity, the electrical performance of flexoelectric microbeams is larger under bending. In contrast, the electrical power for a structure under compression becomes larger with piezoelectricity.
In this thesis, a new approach is developed for applications of shape optimization on the time harmonic wave propagation (Helmholtz equation) for acoustic problems. This approach is introduced for different dimensional problems: 2D, 3D axi-symmetric and fully 3D problems. The boundary element method (BEM) is coupled with the isogeometric analysis (IGA) forming the so-called (IGABEM) which speeds up meshing and gives higher accuracy in comparison with standard BEM. BEM is superior for handling unbounded domains by modeling only the inner boundaries and avoiding the truncation error, present in the finite element method (FEM) since BEM solutions satisfy the Sommerfeld radiation condition automatically. Moreover, BEM reduces the space dimension by one from a volumetric three-dimensional problem to a surface two-dimensional problem, or from a surface two-dimensional problem to a perimeter one-dimensional problem. Non-uniform rational B-splines basis functions (NURBS) are used in an isogeometric setting to describe both the CAD geometries and the physical fields.
IGABEM is coupled with one of the gradient-free optimization methods, the Particle Swarm Optimization (PSO) for structural shape optimization problems. PSO is a straightforward method since it does not require any sensitivity analysis but it has some trade-offs with regard to the computational cost. Coupling IGA with optimization problems enables the NURBS basis functions to represent the three models: shape design, analysis and optimization models, by a definition of a set of control points to be the control variables and the optimization parameters as well which enables an easy transition between the three models.
Acoustic shape optimization for various frequencies in different mediums is performed with PSO and the results are compared with the benchmark solutions from the literature for different dimensional problems proving the efficiency of the proposed approach with the following remarks:
- In 2D problems, two BEM methods are used: the conventional isogeometric boundary element method (IGABEM) and the eXtended IGABEM (XIBEM) enriched with the partition-of-unity expansion using a set of plane waves, where the results are generally in good agreement with the linterature with some computation advantage to XIBEM which allows coarser meshes.
-In 3D axi-symmetric problems, the three-dimensional problem is simplified in BEM from a surface integral to a combination of two 1D integrals. The first is the line integral similar to a two-dimensional BEM problem. The second integral is performed over the angle of revolution. The discretization is applied only to the former integration. This leads to significant computational savings and, consequently, better treatment for higher frequencies over the full three-dimensional models.
- In fully 3D problems, a detailed comparison between two BEM methods: the conventional boundary integral equation (CBIE) and Burton-Miller (BM) is provided including the computational cost. The proposed models are enhanced with a modified collocation scheme with offsets to Greville abscissae to avoid placing collocation points at the corners. Placing collocation points on smooth surface enables accurate evaluation of normals for BM formulation in addition to straightforward prediction of jump-terms and avoids singularities in $\mathcal{O} (1/r)$ integrals eliminating the need for polar integration. Furthermore, no additional special treatment is required for the hyper-singular integral while collocating on highly distorted elements, such as those containing sphere poles. The obtained results indicate that, CBIE with PSO is a feasible alternative (except for a small number of fictitious frequencies) which is easier to implement. Furthermore, BM presents an outstanding treatment of the complicated geometry of mufflers with internal extended inlet/outlet tube as an interior 3D Helmholtz acoustic problem instead of using mixed or dual BEM.
Das Ziel der Arbeit ist, eine mögliche Verbesserung der Güte der Lebensdauervorhersage für Gusseisenwerkstoffe mit Kugelgraphit zu erreichen, wobei die Gießprozesse verschiedener Hersteller berücksichtigt werden.
Im ersten Schritt wurden Probenkörper aus GJS500 und GJS600 von mehreren Gusslieferanten gegossen und daraus Schwingproben erstellt.
Insgesamt wurden Schwingfestigkeitswerte der einzelnen gegossenen Proben sowie der Proben des Bauteils von verschiedenen Gussherstellern weltweit entweder durch direkte Schwingversuche oder durch eine Sammlung von Betriebsfestigkeitsversuchen bestimmt.
Dank der metallografischen Arbeit und Korrelationsanalyse konnten drei wesentliche Parameter zur Bestimmung der lokalen Dauerfestigkeit festgestellt werden: 1. statische Festigkeit, 2. Ferrit- und Perlitanteil der Mikrostrukturen und 3. Kugelgraphitanzahl pro Flächeneinheit.
Basierend auf diesen Erkenntnissen wurde ein neues Festigkeitsverhältnisdiagramm (sogenanntes Sd/Rm-SG-Diagramm) entwickelt.
Diese neue Methodik sollte vor allem ermöglichen, die Bauteildauerfestigkeit auf der Grundlage der gemessenen oder durch eine Gießsimulation vorhersagten lokalen Zugfestigkeitswerte sowie Mikrogefügenstrukturen besser zu prognostizieren.
Mithilfe der Versuche sowie der Gießsimulation ist es gelungen, unterschiedliche Methoden der Lebensdauervorhersage unter Berücksichtigung der Herstellungsprozesse weiterzuentwickeln.
Compactly, this thesis encompasses two major parts to examine mechanical responses of polymer compounds and two dimensional materials:
1- Molecular dynamics approach is investigated to study transverse impact behavior of polymers, polymer compounds and two dimensional materials.
2- Large deflection of circular and rectangular membranes is examined by employing continuum mechanics approach.
Two dimensional materials (2D), including, Graphene and molybdenum disulfide (MoS2), exhibited new and promising physical and chemical properties, opening new opportunities to be utilized alone or to enhance the performance of conventional materials. These 2D materials have attracted tremendous attention owing to their outstanding physical properties, especially concerning transverse impact loading.
Polymers, with the backbone of carbon (organic polymers) or do not include carbon atoms in the backbone (inorganic polymers) like polydimethylsiloxane (PDMS), have extraordinary characteristics particularly their flexibility leads to various easy ways of forming and casting. These simple shape processing label polymers as an excellent material often used as a matrix in composites (polymer compounds).
In this PhD work, Classical Molecular Dynamics (MD) is implemented to calculate transverse impact loading of 2D materials as well as polymer compounds reinforced with graphene sheets. In particular, MD was adopted to investigate perforation of the target and impact resistance force . By employing MD approach, the minimum velocity of the projectile that could create perforation and passes through the target is obtained. The largest investigation was focused on how graphene could enhance the impact properties of the compound. Also the purpose of this work was to discover the effect of the atomic arrangement of 2D materials on the impact problem. To this aim, the impact properties of two different 2D materials, graphene and MoS2, are studied. The simulation of chemical functionalization was carried out systematically, either with covalently bonded molecules or with non-bonded ones, focusing the following efforts on the covalently bounded species, revealed as the most efficient linkers.
To study transverse impact behavior by using classical MD approach , Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software, that is well-known among most researchers, is employed. The simulation is done through predefined commands in LAMMPS. Generally these commands (atom style, pair style, angle style, dihedral style, improper style, kspace style, read data, fix, run, compute and so on) are used to simulate and run the model for the desired outputs. Depends on the particles and model types, suitable inter-atomic potentials (force fields) are considered. The ensembles, constraints and boundary conditions are applied depends upon the problem definition. To do so, atomic creation is needed. Python codes are developed to generate particles which explain atomic arrangement of each model. Each atomic arrangement introduced separately to LAMMPS for simulation. After applying constraints and boundary conditions, LAMMPS also include integrators like velocity-Verlet integrator or Brownian dynamics or other types of integrator to run the simulation and finally the outputs are emerged. The outputs are inspected carefully to appreciate the natural behavior of the problem. Appreciation of natural properties of the materials assist us to design new applicable materials.
In investigation on the large deflection of circular and rectangular membranes, which is related to the second part of this thesis, continuum mechanics approach is implemented. Nonlinear Föppl membrane theory, which carefully release nonlinear governing equations of motion, is considered to establish the non-linear partial differential equilibrium equations of the membranes under distributed and centric point loads. The Galerkin and energy methods are utilized to solve non-linear partial differential equilibrium equations of circular and rectangular plates respectively. Maximum deflection as well as stress through the film region, which are kinds of issue in many industrial applications, are obtained.
Bauablaufplänen kommt bei der Realisierung von Bauprojekten eine zentrale Rolle zu. Sie dienen der Koordination von Schnittstellen und bilden für die am Projekt Beteiligten die Grundlage für ihre individuelle Planung. Eine verlässliche Terminplanung ist daher von großer Bedeutung, tatsächlich sind aber gerade Bauablaufpläne für ihre Unzuverlässigkeit bekannt.
Aufgrund der langen Vorlaufzeiten bei der Planung von Bauprojekten sind zum Zeitpunkt der Planung viele Informationen nur als Schätzwerte bekannt. Auf der Grundlage dieser geschätzten und damit mit Unsicherheiten behafteten Daten werden im Bauwesen deterministische Terminpläne erstellt. Kommt es während der Realisierung zu Diskrepanzen zwischen Schätzungen und Realität, erfordert dies die Anpassung der Pläne. Aufgrund zahlreicher Abhängigkeiten zwischen den geplanten Aktivitäten können einzelne Planänderungen vielfältige weitere Änderungen und Anpassungen nach sich ziehen und damit einen reibungslosen Projektablauf gefährden.
In dieser Arbeit wird ein Vorgehen entwickelt, welches Bauablaufpläne erzeugt, die im Rahmen der durch das Projekt definierten Abhängigkeiten und Randbedingungen in der Lage sind, Änderungen möglichst gut zu absorbieren. Solche Pläne, die bei auftretenden Änderungen vergleichsweise geringe Anpassungen des Terminplans erfordern, werden hier als robust bezeichnet.
Ausgehend von Verfahren der Projektplanung und Methoden zur Berücksichtigung von Unsicherheiten werden deterministische Terminpläne bezüglich ihres Verhaltens bei eintretenden Änderungen betrachtet. Hierfür werden zunächst mögliche Unsicherheiten als Ursachen für Änderungen benannt und mathematisch abgebildet. Damit kann das Verhalten von Abläufen für mögliche Änderungen betrachtet werden, indem die durch Änderungen erzwungenen angepassten Terminpläne simuliert werden. Für diese Monte-Carlo-Simulationen der angepassten Terminpläne wird sichergestellt, dass die angepassten Terminpläne logische Weiterentwicklungen des deterministischen Terminplans darstellen. Auf der Grundlage dieser Untersuchungen wird ein stochastisches Maß zur Quantifizierung der Robustheit erarbeitet, welches die Fähigkeit eines Planes, Änderungen zu absorbieren, beschreibt. Damit ist es möglich, Terminpläne bezüglich ihrer Robustheit zu vergleichen.
Das entwickelte Verfahren zur Quantifizierung der Robustheit wird in einem Optimierungsverfahren auf Basis Genetischer Algorithmen angewendet, um gezielt robuste Terminpläne zu erzeugen. An Beispielen werden die Methoden demonstriert und ihre Wirksamkeit nachgewiesen.
The current thesis presents research about new methods of citizen participation based on digital technologies. The focus on the research lies on decentralized methods of participation where citizens take the role of co-creators. The research project first conducted a review of the literature on citizen participation, its origins and the different paradigms that have emerged over the years. The literature review also looked at the influence of technologies on participation processes and the theoretical frameworks that have emerged to understand the introduction of technologies in the context of urban development. The literature review generated the conceptual basis for the further development of the thesis.
The research begins with a survey of technology enabled participation applications that examined the roles and structures emerging due to the introduction of technology. The results showed that cities use technology mostly to control and monitor urban infrastructure and are rather reluctant to give citizens the role of co-creators. Based on these findings, three case studies were developed. Digital tools for citizen participation were conceived and introduced for each case study. The adoption and reaction of the citizens were observed using three data collection methods.
The results of the case studies showed consistently that previous participation and engagement with informal citizen participation are a determinining factor in the potential adoption of digital tools for decentralized engagement. Based on these results, the case studies proposed methods and frameworks that can be used for the conception and introduction of technologies for decentralized citizen participation.
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.
Open Innovation in kleinen und mittleren Unternehmen (KMU) hat sich stark ausdifferenziert. Dabei zeigt die Empirie, dass KMU unterschiedliche Wege in der offenen Entwicklung von Innovationen begehen. Um die bestehende Literatur zu erweitern, wurden mit dieser Dissertation die Ziele verfolgt 1) offene Innovationsaktivitäten in KMU aus einer Prozessperspektive aufzudecken und genau zu beschreiben und 2) zu erklären, warum sich die Öffnung von Innovationsprozessen in KMU unterscheidet. Dafür wurde auf eine multiple Fallstudienanalyse zurückgegriffen. Untersuchungsobjekte waren kleine etablierte High-Tech Unternehmen aus den neuen Bundesländern. Die Ergebnisse zeigen sechs Prozessmodelle der offenen Innovationsentwicklung, beschrieben als Open Innovation Muster. Deskriptionen dieser Muster unter Berücksichtigung von formenden Innovationsaktivitäten, ausgetauschtem Wissen, beteiligten externen Akteuren und Gründen für und gegen Open Innovation vermitteln ein über den bisherigen Forschungsstand hinausgehendes Verständnis von Open Innovation in KMU. Zudem zeigen die Ergebnisse, dass die Entrepreneurial Orientation erklärt, warum KMU bei der Ausgestaltung von offenen Innovationsprozessen unterschiedlich vorgehen. In der Dissertation wird detailliert dargelegt, welche Open Innovation Muster sich anhand der Entrepreneurial Orientation von KMU (nicht-entrepreneurial bis entrepreneurial) zeigen. Die Ergebnisse liefern sowohl wissenschaftliche Implikationen, als auch Handlungsempfehlungen für die Unternehmenspraxis.
The modern industries of the 19th and 20th centuries had multiple effects on the spatial transformation of cities and regions. The past decade has witnessed increasing scholarly and governmental attempts toward conserving modern industrial heritage in the so-called Global North, with the goal, among others, of leveraging this heritage as a driver for urban economic development. In Egypt, the process continues to lag behind; on the one hand, this is due to the perplexing official recognition of the (in)tangible witnesses of modern industries. On the other hand, the official recognition and previous publications focus predominantly on weighing the significance of industrial structures based on their monumental architectural aesthetics. Their historical urban role and spatial attributes as part of urban heritage have yet to be seriously acknowledged. Accordingly, this hinders the integration of the extant industrial sites into the broader debate surrounding urban conservation, leaving them vulnerable to decay and destruction.
This dissertation steers away from the singular investigation of selective modern industrial sites to recall their historical spatial development on a city scale. This is effected by investigating a case study - the Egyptian port city of Alexandria. With the limited secondary data available on modern industries in Alexandria, this dissertation relied predominantly on primary sources. The author collected and leveraged both quantitative and qualitative data to recontextualize modern industries in terms of their spatial dynamics, order, and rationale within cities’ transformation.
By recalling historical spatial development in Alexandria, the contribution of this dissertation lies in highlighting what the author refers to as the Omitted Heritage. This is defined by the modern industries in Egypt that are intentionally, unintentionally, and forgetfully excluded in terms of physical documentation, evaluation, appreciation, and integration within urban development plans. The method used excavated the richness of the established modern industries in Alexandria in terms of their quantity and diversity, which would have otherwise remained largely forgotten. The contextualization of modern industries unveiled spatial periodization, spatial dynamics, and conceptual development. The study draws on important analytical aspects that transcend the sites’ boundaries, elevating their significance to the municipal, regional, national, and even global levels. Its recommendations for further research are also divided into those levels.
Revisiting vernacular technique: Engineering a low environmental impact earth stabilisation method
(2022)
The major drawbacks of earth as a construction material — such as its low water stability and moderate strength — have led mankind to stabilize earth. Different civilizations developed vernacular techniques mainly focussing on lime, pozzolan or gypsum stabilization. Recently, cement has become the most commonly used additive in earth stabilization as it improves the strength and durability of plain earth. Also, it is a familiar and globally available construction material. However, using cement as an additive reduces the environmental advantages of earth and run counter to global targets regarding the reduction of CO2 emissions. Alternatives to cement stabilization are currently neither efficient enough to reduce its environmental impact nor allow the possibility of obtaining better results than those of cement. As such, this thesis deals with the rediscovery of a reverse engineering approach for a low environmental impact earth stabilization technique, aiming to replace cement in earth stabilization.
The first step in the method consists in a comprehensive review of earth stabilization with regards to earthen building standards and soil classification, which allows us to identify the research gap. The review showed that there is great potential in using other additives which result in similar improvements as those achieved by cement. However, the studies that have been conducted so far either use expansive soils, which are not suitable for earth constructions or artificial pozzolans that indirectly contribute to CO2 emissions. This is the main research gap.
The key concept for the development in the second step of the method is to combine vernacular additives to both improve the strength and durability of plain earth and to reduce the CO2 emissions. Various earth-mixtures were prepared and both development and performance tests were done to investigate the performance of this technique. The laboratory analyses on mix-design have proven a high durability and the results show a remarkable increase in strength performance. Furthermore, a significant reduction in CO2 emissions in comparison to cement stabilization could be shown.
The third step of the method discusses the results drawn from the experimental programme. In addition, the potential of the new earth mixture with regards to its usability in the field of building construction and architectural design is further elaborated on.
The method used in this study is the first of its kind that allows investors to avoid the very time-consuming processes such as finding a suitable source for soil excavation and soil classification. The developed mixture has significant workability and suitability for production of stabilized earthen panels — the very first of its kind. Such a panel is practically feasible, reasonable, and could be integrated into earthen building standards in general and in particular to DIN 18948, which is related to earthen boards and published in 2018.