Lehrstuhl Baumechanik

Permanent URI for this collection

http://hdl.handle.net/2003/173

Browse

Now showing 1 - 20 of 23

Numerical optimisation of damage in extrusion processes
(2023-09-17) Guhr, Fabian; Gitschel, Robin; Barthold, Franz-Joseph; Tekkaya, A. Erman
Numerical optimisation is applied to rod extrusion in order to generate optimal parameter sets which result in reduced damage accumulation. A brief overview of academic applications for damage optimisation is given. Their restrictions are reflected upon, leading to the proposed framework utilising the commercial software Abaqus FEA, which enables optimisation of industrial problems with frictional contact. The framework is setup modularly to enable arbitrary choices of design variables, such as geometric parameters, and process parameters like friction coefficients or boundary conditions. The optimisation strategy is applied to forward hollow extrusion. Compared to forward rod extrusion, an additional design variable, that is, the mandrel radius, is introduced into the forming process, which increases the design space.
Gradient‐based determination of principal design influences on composite structures
(2023-09-25) Liedmann, Jan; Barthold, Franz-Joseph; Gerzen, Nikolai
This work deals with the computation of design sensitivities of elastic solid-shell structures extended to anisotropic layered composite structures. Design sensitivities concerning fiber angles and layer thicknesses are derived and quantitatively determined in the context of the finite element method. The anisotropic analysis model is founded on a sophisticated solid-shell formulation based on reduced integration and is extended to discretize the composite with only one element over the element thickness by means of multiple integration points. This can be understood as a special case of equivalent-single-layer theories. Examination of system response sensitivity matrices using methods from principal component analysis, such as singular value decomposition, is used to identify crucial design changes corresponding to major changes in the structural behavior of the composite. This procedure is termed as sensitivity based design exploration. Results are discussed by reference to simple academic examples.
Geometrical design modes of dynamic structures
(2023-09-28) Ghasemi, Seyed Ali; Liedmann, Jan; Barthold, Franz-Joseph
In this work, a hybrid, that is, discrete in time and continuous in space, sensitivity analysis for dynamic structures using isogeometric analysis is presented. The main focus is placed on using a direct differentiation technique to derive sensitivity matrices for displacement, velocity and acceleration. To gain further understanding of the sensitivity information, a singular value decomposition is used to decompose these sensitivity matrices. The findings are exemplified on an academic example.
Sensitivity and optimisation of damage in forming processes
(2024) Guhr, Fabian; Barthold, Franz-Joseph; Menzel, Andreas
Die Herstellung technischer Komponenten in der heutigen Industrie erfordert ein großes Maß an Wissen, um Teile mit den gewünschten Eigenschaften zu produzieren. Dieses benötige Wissen umfasst das Materialverhalten, den Herstellungsprozess, sowie die Belastung, welche das Bau-teil im Einsatz erfährt. Eine Kombination dieser Faktoren ermöglicht es dem Ingenieur, ein Pro-dukt zu entwerfen, welches den Anforderungen der jeweiligen Anwendung gerecht wird. Elasti-sche und plastische Materialeigenschaften sind heutzutage reichlich erforscht. Schädigungs-mechanik stellt jedoch weiterhin eine anspruchsvolle Herausforderung dar und nimmt eine wich-tige Rolle in der aktuellen Forschung ein. Schädigung wird als eine Ansammlung von Defekten auf der Mikroskala verstanden, welche zu einer Verschlechterung des makroskopischen Mate-rialverhaltens führt. Die Berücksichtigung von Schädigungsmodellierung im Konstruktionspro-zess ermöglicht die Vorhersage des Schädigungszustandes, welcher durch den Fertigungspro-zess entsteht. Die Schädigung kann durch Anpassung von Prozessparametern reduziert wer-den, um Teile zu erzeugen, die eine geringere Schädigungsanreicherung aufweisen und in der Anwendung schädigungstoleranter sind. Hier ermöglicht der Einsatz numerischer Optimierung die automatische Generierung schädigungstoleranter Prozesse und Bauteile. Diese Arbeit befasst sich mit der numerischen Schädigungsoptimierung und lässt sich in zwei Bereiche einteilen. Der erste Bereich befasst sich mit den akademischen Herausforderungen eines solchen Optimierungsproblems. Ein nicht-lokales duktiles Schädigungsmodell wird mit Sensitivitätsinformationen angereichert, um Formoptimierung zu ermöglichen. Die analytische Herleitung der Gradienten erlaubt die Anwendung gradientenbasierter Optimierungsstrategien, wodurch die Rechenzeit erheblich reduziert wird. Dieser Ansatz ist zwar rechnerisch effizient und elegant für die Herleitung der Sensitivitätsinformationen, der Anwendungsbereich ist jedoch auf akademische Probleme beschränkt. Daher befasst sich der zweite Bereich dieser Arbeit mit den industriellen Herausforderungen. Dafür wird eine zusätzliche Optimierungsumgebung um eine kommerzielle Finite Elemente Software herum entwickelt. Diese ermöglicht eine Schädi-gungsoptimierung von Umformprozessen, sodass Parameterkombinationen gefunden werden können, die Bauteile mit geringerer Schädigungsanreicherung erzeugen.
Experiments and modelling of the load capacity of green wood
(2023-05-31) Loske, Simon; Muench, Ingo
The material properties of green wood in the shaft of vital trees differ significantly from the generally known material properties of technically processed, dried wood. Furthermore, completely different residual stresses and fracture mechanisms are present in the natural full cross-section [1]. The properties also depend on the tree species. Our work focuses on green wood from european beech (Fagus sylvatica). A large number of experiments on small test specimens of green wood are known from [2]. We present both, experiments on small and large-scaled specimens. Latter are bending test on trunks with full cross-section. Combining results and considering micro-mechanical properties of cellular wood components [3], a computational model is fitted to our experimental results. This aspect influences the fracture resistance of a tree and should be representable in a computational model. This is particularly important in order to better assess the risk of building on vital trees.
Geometric and material sensitivities for elasto-plasticity including non-local damage regularisation
(2023-05-31) Guhr, Fabian; Barthold, Franz-Joseph
Sensitivity analysis is applied to a regularised non-local ductile damage model. A variational approach is utilised to derive the analytical gradients of different objectives with respect to either geometrical of material parameters. Due to the definition of the material model, enhanced algorithmic treatments are necessary to capture its history dependent nature within the sensitivity computation. The gradient information with respect to the geometrical parameters are used to derive damage tolerant geometries in shape optimisation using Sequential Quadratic Programming (SQP). The sensitivities with respect to the material parameters are used to analyse the response and impact of certain material parameters of the model during loading and unloading of a specimen.
Remarks on wave propagation in an acoustic metamaterial modeled as a relaxed micromorphic continuum
(2023-05-31) Voss, Jendrik; Rizzi, Gianluca; Demetriou, Plastiras; Neff, Patrizio; Madeo, Angela
In order to describe elastic waves propagation in metamaterials, i.e. solids with heterogeneities or microstructure, it is necessary to consider non-local or higher-order models. The relaxed micromorphic model (RMM) proposed here can describe these effects as a continuous material with enriched kinematics. We present a new unit cell giving rise to a metamaterial for acoustic application. The microstructure is engineered to show a band-gap in the low acoustic regime (600-2000 Hz) for which waves cannot propagate through the material. We concentrate on the size effects to make full advantage of the particularly beneficial structure that the model provides. The RMM material parameters are fitted using a new algorithm relying on cutoffs and asymptotes (obtained via a Bloch-Floquet analysis). In particular, by enhancing the kinetic energy of the model with a new inertia term, we enable decreasing curves (modes with negative group velocity).
Modeling a labyrinthine acoustic metamaterial through an inertia-augmented relaxed micromorphic approach
(2023-02-28) Voss, Jendrik; Rizzi, Gianluca; Neff, Patrizio; Madeo, Angela
We present an inertia-augmented relaxed micromorphic model that enriches the relaxed micromorphic model previously introduced by the authors via a term Curl P⋅ in the kinetic energy density. This enriched model allows us to obtain a good overall fitting of the dispersion curves while introducing the new possibility of describing modes with negative group velocity that are known to trigger negative refraction effects. The inertia-augmented model also allows for more freedom on the values of the asymptotes corresponding to the cut-offs. In the previous version of the relaxed micromorphic model, the asymptote of one curve (pressure or shear) is always bounded by the cut-off of the following curve of the same type. This constraint does not hold anymore in the enhanced version of the model. While the obtained curves’ fitting is of good quality overall, a perfect quantitative agreement must still be reached for very small wavelengths that are close to the size of the unit cell.
Shape optimised geometries for ductile damaging materials
(2021-12-14) Guhr, Fabian; Barthold, Franz-Joseph
Shape optimisation is utilised to generate damage resistant structures. By means of a variational approach, the analytical gradients for an elasto-plastic material model with regularised damage properties are derived. Due to the complexity of the underlying material model, the application of the variational approach requires additional handling of the history field. The gradients are then used for Sequential Quadratic Programming (SQP) which is applied to shape optimisation and thus generation of damage optimised geometries.
Analytical solution of the uniaxial extension problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)
(2021-11-17) Rizzi, Gianluca; Hassam Khan, Ionel-Dumitrel Ghiba; Madeo, Angela; Neff, Patrizio
We derive analytical solutions for the uniaxial extension problem for the relaxed micromorphic continuum and other generalized continua. These solutions may help in the identification of material parameters of generalized continua which are able to disclose size effects.
Finite element modelling of UHPC under pulsating load using X-ray computed tomography based fiber distributions
(2021-12-18) Mellios, Nikolaos; Oesch, Tyler; Spyridis, Panagiotis
The benefits of including fibers in ultra-high performance concrete (UHPC) are attributed to their good bond with the matrix and, hence, an optimal utilization of their properties. At the same time, though, fiber reinforcement may contribute to anisotropy in the composite material and induce weak areas. The influence of the fibers’ orientation on the material properties is a matter of current scientific discourse and it is known to play a vital role in structural design. In the case studies presented herein, mechanical laboratory tests using pulsating load regimes on UHPC with a strength of more than 200 MPa were simulated by use of finite element models. The orientations of the fibers were measured for each test sample prior to failure using an X-ray computed tomography (CT) scanner, and these orientations are explicitly implemented into the model. The paper discusses the methodology of merging data retrieved by CT image processing and state-of-the-art FE simulation techniques Moreover, the CT scanning was carried out throughout the testing procedure, which further enables the comparison of the mechanical tests and the FE models in terms of damage propagation and failure patterns. The results indicate that the overall fiber configuration and behavior of the samples can be realistically modelled and validated by the proposed CT-FE coupling, which can enhance the structural analysis and design process of elements produced with steel fiber reinforced and UHPC materials.
Elastic-plastic design sensitivities based on variational analysis and applications in optimal specimen design
(2021) Liedmann, Jan; Barthold, Franz-Joseph; Brünig, Michael
Voranschreitender technologischer Fortschritt fordert hohe Ansprüche an ingenieurtechnische Strukturen und Materialien. Dabei ist es wichtig, die Produktionskosten gering zu halten und gleichzeitig höchste Sicherheit in der praktischen Anwendung zu gewährleisten. Auch logistische und ökologische Aspekte spielen eine wichtige Rolle. Die richtige Wahl und Ausnutzung des Potentials der verwendeten Materialien ist in diesen Zusammenhängen enorm wichtig. Die computergestützte Optimierung von Bauteilen und Materialien ist dem Gebiet der Strukturoptimierung zuzuordnen, welche es ermöglicht, mechanische Strukturen hinsichtlich gewählter Eigenschaften zu verbessern und gleichzeitig wichtige Einschränkungen zu berücksichtigen. Dafür muss das zu verändernde Design definiert und gewünschte Zielwerte und Nebenbedingungen mathematisch formuliert werden. Dies erfordert zum einen Wissen über den Grad der Beanspruchung des analysierten Bauteils und zum anderen müssen die mechanischen Vorgänge innerhalb des verwendeten Materials gut verstanden und im Rahmen mathematischer Modelle abbildbar sein. Vor allem ungünstige Phänomene, wie z.B. plastisches Fließen, Schädigung oder Ermüdung, die letztendlich zum Strukturversagen führen können, sind es wert detailliert analysiert zu werden. Die Entwicklung von Modellen zur Beschreibung mechanischer Phänomene ist langjährige wissenschaftliche Tradition und wird stets weiterentwickelt. Die Durchführung wissenschaftlicher Experimente ist in diesem Zusammenhang unabdinglich und sollte auf das zu untersuchende mechanische Phänomen zugeschnitten sein. In dieser Arbeit geht es um die Formoptimierung biaxialer Versuchskörper zur Charakterisierung von Schädigung duktiler metallischer Werkstoffe. Duktile Schädigung und die treibenden mikromechanischen Mechanismen sind abhängig vom Spannungszustand. Daher soll die Form der Biaxialprobe so verändert werden, dass sich während der Versuche bestimmte und möglichst homogene Spannungszustände einstellen. Hierzu wird ein effizientes computergestütztes Modell aufbereitet, das große elastoplastische Deformationen berücksichtigt und im Rahmen eines gradientenbasierten Optimierungsverfahrens die benötigten Sensitivitätsinformationen bezüglich der Formänderung der Probe liefert. Die Bestimmung der Sensitivitätsinformationen erfolgt mittels eines variationellen Ansatzes und erfordert tiefes Verständnis der Grundgleichungen des mechanischen Modells. Zur Validierung der resultierenden optimalen Geometrien werden Experimente durchgeführt und mittels digitaler Bildkorrelation aufgezeichnet. Anschließend werden hochauflösende Bilder der Bruchflächen untersucht, die mittels eines Rasterelektronenmikroskops aufgenommen wurden, um Rückschlüsse auf den Spannungszustand kurz vor dem Versagen zu ziehen.
A finite element formulation for a simplified, relaxed micromorphic continuum model
(2021-01-25) Chejanovsky, Adam; Münch, Ingo; Neff, Patrizio
We discuss a simplified problem derived from the relaxed micromorphic continuum model in two dimensions. The model captures important aspects of the micromorphic approach even as a degeneration of the bulk model. Typically, the employed mechanical strain combines the gradient of displacements with the microdistortion field. The interaction between both fields is ruled by the minimization of the overall free energy, where we employ the Curl of the microdistortion. The Curl significantly influences the resulting equations for the balance of linear and angular momentum. Further, we explain the necessity of an extended finite element method. Finite elements based on solely the H1‐Hilbert space are not sufficient for the efficient approximation of the Curl based microdistortion. Therefore, we suggest using a hybrid scheme employing both, H1 and H(Curl) based functions. The resulting hybrid element formulation is successfully tested for a problem with a predefined Dirichlet boundary condition.
Shape optimization of the X0‐specimen for biaxial experiments
(2021-01-25) Liedmann, Jan; Gerke, Steffen; Barthold, Franz-Joseph; Brünig, Michael
The mechanical damage and fracture behavior of ductile sheet metals strongly depend on the stress state and intensity. Thus, for adequate characterization of the material behavior, it is crucial to have specimens that cover different and preferably distinct stress states, especially in the inelastic domain. In this paper, the geometry of the X0‐specimen is optimized to achieve a distinct stress triaxiality distribution in the region of damage and fracture occurrence, depending on two different load cases in a biaxial testing environment. The shape optimization is gradient based and the gradients of the objective and constraint functions are computed analytically by means of variational principles. The resulting geometries show improvements in terms of the intensity of the stress state numerically as well as experimentally.
Damage optimisation for air bending
(2021-01-25) Guhr, Fabian; Barthold, Franz-Joseph
Load and shape optimisation are applied to the process of air bending to optimise the damage state in the formed component. The enhanced process of elastomer bending is optimised, which yields a reduced damage state due to the superimposed radial stresses in the critical area of the forming process. The optimisation presented here is twofold. First, the elastomer is replaced by nodal loads to generate optimised loads for a reduced damage state. Second, the elastomer itself is optimised via shape optimisation by adjusting the layer for two kinds of elastomer of varying stiffness. The optimisation is accomplished with the commercial FEM software Abaqus as the solver for the mechanical problem and Matlab is used for optimisation.
Probabilistic damage simulation for strengthening design of concrete structures
(2021-01-25) Molod, Mohammad Amin; Barthold, Franz-Joseph; Spyridis, Panagiotis
Shape memory alloy (SMA) is a smart material that can be applied as an internal and external reinforcement of reinforced concrete flexural elements in order to increase ductility and strength of the members. Column‐beam joint is a critical section of a concrete structure which under seismic and unexpected heavy loads may lead to failure of entire of the structure. Therefore, this numerical investigation aims to increase strength and mitigate risk of failure of the joint by employment of SMA plate. To do so, an experimentally investigated joint under 1000 load combinations has been simulated in Ansys APDL. Each load combo contained two axial loads and one bending moment; load values have been randomly selected through a procedure in MATLAB. Some nodes in plastic hinge region of the joint were chosen as control points. Generated load values were applied in the simulation, and stress of the control nodes was recorded. This process continued for all 1000 combos. Then, obtained results were imported into MATLAB for a probabilistic analysis. Probability of 0.95 quantile of stress of each node was calculated in order to design the required plate thickness at each node. Some numerical examples were applied on the designed plate. Results demonstrated that the designed SMA plate gets the risk of failure from the joint away and increase strength of the joint.
Strengthening reinforced concrete column-beam joints with modular shape memory alloy plate optimized through probabilistic damage prediction
(2021) Molod, Mohammad Amin Esmail; Barthold, Franz-Joseph; Spyridis, Panagiotis
Column-beam joints are one of the most critical zones of concrete structures, especially under unpredicted heavy loads and lateral loads such as seismic. Failure of the joints can even lead to failure of structures in their entirety. The low strength capacity of concrete is a reason of sensitivity of the region. Shape memory alloy (SMA) plates can be employed in order to overcome this weakness and increase the stiffness of joints in existing structures. SMA is a smart material whose functionality, workability and its self-healing feature are under investigation by scientists in the field of structural engineering. In fact, there are two types of alloy: i) superelastic shape memory alloy and ii) shape memory effect that is sensitive to temperature, but it is out of the topic of the research. However, a superelastic form is the most common type of alloy in the field of structural engineering that can be used not only as external reinforcement bolted to the concrete surface but also as internal reinforcement embedded within the concrete elements. The author of this numerical research attempted to implement a plate form of the alloy as external reinforcement to increase stiffness and ductility of the joint. To do so, an experimentally investigated concrete column-beam joint has been modelled in Ansys, and it was loaded under a large number of randomly selected load combinations. The plate initially was designed with a uniform thickness and length in the plastic hinge region of the joint under the critical load combination. Then, probabilistic analysis was carried out to optimize the plate’s thickness. To that end, the stress values of thirty-five predefined nodes on the plate surface were recorded under each load combinations. Results were imported into MATLAB software to run the probabilistic analysis and specifying 0.95 quantile of the stored stresses of the nodes. Design optimization was also carried out based on the probabilistic results in order to design the thickness of the plate at different control nodes. During the course of the research, a set of necessary additional trials have been carried out, as for example with regards to the proper Ansys element type selection for reinforced concrete, determination of limit state functions, and to assess the most suitable parallel processing setup. A fastening technique was also employed to connect the optimized SMA plate to the surface of the concrete joint. Finally, some numerical examples have been run in order to check to what extend the utilized method worked properly. The procedure was applied twice; i) when the load combinations were applied in cyclic form and ii) when the load combinations were exerted in reverse cyclic form. Therefore, two optimized SMA have been designed and examined. The results of the analyses showed that the employed technique enhanced the strength of the joint considerably so that the cracking load of the system reinforced with optimized SMA plate under cyclic loading was 1.4 times greater than the benchmark. The load-carrying capacity of the reinforced system in the elastic regime was higher than the unreinforced structure, and the capability in the plastic regime was even higher. Indicatively, the load-carrying capacity of the reference system at a displacement of 32 mm was approximately 98 kN, whereas the respective resistance value was approximately 66 kN in the system without the plate. Besides, the existence of the plate led to transition of the failure zone from the joint to the beam span, which leads to a lower risk of failure of the entire structure. As a result, the main focus of the research was to describe a novel method that allows for a probability-based prediction of damage in concrete structures that can facilitate the assessment and design of degraded structures under risk of failure.
Load optimisation for air bending in the context of damage reduction
(2019-11-12) Guhr, Fabian; Barthold, Franz-Joseph; Meya, Rickmer; Tekkaya, A. Erman
Load optimisation applied to air bending is used to optimise the damage state in the formed component. In [1], elastomer bending is presented, where superposed stresses due to the reaction forces of the elastomer cushion lead to reduced damage growth. Replacing the elastomer cushion with compressive loads allows for optimisation of these loads such that the damage, estimated with the stress triaxiality, is reduced. The optimisation is accomplished with the commercial FEM‐Software Abaqus as the solver for the mechanical problem where Sequential Quadratic Programming (SQP) is used within Matlab to generate improved loads.
Optimal material design based on variational sensitivity analysis
(2018) Kijanski, Wojciech; Barthold, Franz-Joseph; Schröder, Jörg
Today's state of the art within industrial applications requires the usage of efficient and high-performance materials, which are optimally designed in terms of production costs, material savings, fuel consumption or their mechanical behaviour. In many cases, a useful choice of materials of components contributes to the overall performance significantly. Modern materials can not be classified as homogeneous, but are composed of various ingredients. Often, considerations at the structural level are no longer sufficient and investigations on a lower length scale, the so-called material- or microscale, become necessary. Based on experimental data and results, practical experience and available methods for computer-aided simulation and analysis, the responsible design engineer has to decide which ingredients are suitable for a goal-oriented composition of materials. The evaluation of the choice made can be performed based on so-called multiscale methods for structural analysis. These also include the FE2 method, which allows a combined analysis of the macroscopic structural behaviour and the microscopic material behaviour by a numerical homogenisation scheme applied to the microscopic material structure. The work at hand provides an enhancement of methods for the numerical multiscale simulation of the physical behaviour and enables improvements of characteristic properties. This extension leads to the research field of structural optimisation. Apart from sizing, it deals with the optimal design of components in the sense of optimal topological distribution of material as well as shape optimisation. The classical sequence of steps within a structural optimisation process contains the definition of goals, restrictions and design variables as well as the choice of algorithms for mathematical optimisation. The proposed method extends the formulation of a single-scale optimisation task and allows choices of objective functions, constraints and design parameters on multiple scales. Design parameters are for instance characteristic material properties, number and location of holes and inclusions, and geometrical parameters in general. Since the numerical effort within methods for multiscale structural analysis raises with the complexity of referred problems, it is useful to apply efficient methods in the context of structural optimisation. This class of methods includes the so-called gradient based optimisation methods. Within the present work, the required gradient and sensitivity information are derived and provided based on the variational approach for sensitivity analysis. By means of suitable examples and numerical investigations, it is shown that this approach can be classified as performant by nature.
Analysis and applications of variational sensitivity information in structural optimisation
(2014-05-22) Gerzen, Nikolai; Barthold, Franz-Joseph; Bletzinger, Kai-Uwe
Die vorliegende Arbeit befasst sich mit der inneren Struktur der Empfindlichkeiten von mechanischen Strukturen bezüglich geometrischer Veränderungen. Der Begriff innere Struktur der Empfindlichkeiten wird als abkürzende Bezeichnung für die Eigenwerte und Singulärwerte, die entsprechenden Eigenwert- und Singulärwertspektren, sowie die zugehörigen Eigenvektoren und singulären Vektoren der Pseudolast-, Sensitivitäts- und Designgeschwindigkeitsmatrizen eingeführt. Zusammen bilden diese Größen den Kern der Sensitivitätsanalyse und werden sowohl qualitativ als auch quantitativ mit Hilfe der Singulärwertzerlegung (SVD) und Techniken, die aus dem Bereich der Hauptkomponentenanalyse (PCA) bekannt sind, analysiert. Beschrieben wird der Einfluss der Modellbildung, insbesondere die Wahl der Formparametrisierung auf die Lösung der Optimierungsaufgabe. Dieses Wissen ermöglicht es dem entwerfenden Ingenieur das Modell zu verstehen und es systematisch zu verbessern, was gewöhnlich nur auf seiner Erfahrung und Intuition basiert. Die Schwächen der Modellbildung werden identifiziert und verbesserte Parametrisierungen des Designraumes vorgeschlagen. Ein solches Vorgehen, das unter anderem die Interaktion zwischen Mensch und Maschine erfordert, wird auch als Designexploration bezeichnet und stellt den Schwerpunkt der vorliegenden Arbeit dar. Des Weiteren wird eine algorithmische und automatische Behandlung der auf SVD basierten Sensitivitätsinformationen für verschiedene Anwendungen vorgestellt. Im Zusammenhang mit der Modellreduktion wird der vollständige Designraum auf einen Unterraum mit der größtmöglichen Varianz projeziert, um den Informationsgehalt der Sensitivitätszerlegungen zu demonstrieren. Beispiele werden zeigen, dass nur ein Bruchteil der neu definierten Designvariablen benötigt wird, um brauchbare Optimierungsergebnisse zu erzielen. Das Anwendungsgebiet der SVD basierten Sensitivitätsinformationen wird auf die nichtlineare Beulanalyse ausgeweitet. Hierbei werden die singulären Vektoren der Pseudolastmatrix mit den `worst case' Imperfektionen in Verbindung gebracht. Die entwickelten Konzepte werden auf die Formoptimierung von Schalentragwerken angewandt. Das Design solcher Strukturen hat einen großen Einfluss auf ihre Stabilität, Robustheit und ihre Versagenslast. Die variationelle Sensitivitätsanalyse einer nichtlinearen Schale wird durchgeführt. Insbesondere werden die Sensitivitäts- und Pseudolastmatrizen hergeleitet. Es werden nur statische Probleme mit hyperelastischem, auch nichtlinearem, Materialverhalten betrachtet.

Browse

Recent Submissions