Open topics for student theses

We currently offer the following topics for student theses.

The topics mentioned can still be adapted to your interests/preferences if necessary. Also, if you have your own ideas for topics, please feel free to contact us at any time.

Master thesis: Physics-informed neural networks for crack analysis
(Physikalisch informierte neuronale Netze für die Rissmodellierung)

Crack analysis requires to address the stress singularity at the existing crack tip in a cracked domain. This can be challenging in classical finite element methods, as very fine meshes are required close to the crack tip. An alternative approach is to include closed-form solutions, the availability of which is another challenge in fracture mechanics analysis. To overcome the need of discretizing mesh, physics-informed neural networks (PINN), which integrate partial differential equations and boundary conditions of each problem [1] in loss function minimization process, can be used for crack analysis. In this method, in practice, computations are performed for collocation points which are analogous to integration points of finite elements. The main objective of this master thesis is to create a PINN to calculate the stress intensity factor in different cracked domains under tensile and shear loading [2]. The effect of the enrichment of PINN with near crack tip properties will be studied comparatively.

Strong programming skills are required. Preliminary knowledge in the field of Fracture Mechanics is advantageous.

[1] M. Raissi, P. Perdikaris, and G. E. Karniadakis, ‘Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations’, Journal of Computational Physics, vol. 378, pp. 686–707, 2019.
[2] Y. Gu, C. Zhang, P. Zhang, M. V. Golub, and B. Yu, ‘Enriched physics-informed neural networks for 2D in-plane crack analysis: Theory and MATLAB code’, International Journal of Solids and Structures, vol. 276, p. 112321, 2023.

Contact: Dipraj Kadlag, M.Sc.

Master thesis: Implementation, validation and evaluation of a coupled implicit-explicit time integration method
(Implementierung, Validierung und Bewertung hybrider (explizit-implizit) Zeitschrittverfahren)

In structural dynamics, analytical solution of the equation of motion is usually not possible if the excitation force varies arbitrarily with time. Such problems can be tackled by numerical time-stepping methods [1]. In practical engineering problems, domains under study include stiff as well as flexible subdomains. By integrating stiff subdomains with explicit time-stepping methods, restrictions are placed on the size of the time-step. This obstacle can be evaded by integrating the mesh simultaneously using implicit as well as explicit time-integration schemes [2]. In this work, the proposed hybrid method is to be implemented in Matlab to solve a simple 1-dimensional problem. The implementation is to be validated by comparing the results with those obtained using the standard time-stepping schemes, such as central difference method (explicit scheme) and Newmark’s method (implicit scheme).

[1] A.K. Chopra, Dynamics of Structures – Theory and Application to Earthquake Engineering, Pearson Education, Inc., ISBN: 978-0-13-285803-8.
[2] T. Belytschko, R. Mullen, Stability of explicit-implicit mesh partitions in time integration, International Journal for Numerical Methods in Engineering, 1978, Volume: 12, 1575-1586.

Contact: Sharath Nattoji-Shara, M.Sc.

Master thesis: Stabilität und Genauigkeit von numerischen Verfahren zur Beschreibung der Boden-Bauwerk
Interaktion (Stability and accuracy of numerical methods for soil-structure interaction problems)

In dieser Arbeit sind Anwendungen aus dem Bauwesen von Interesse, bei denen sich elastische Wellen im Boden ausbreiten, sodass die Wechselwirkung von Boden und Bauwerk zu berücksichtigen ist. Beispiele sind: Erdbebensimulationen, Bemessung von Maschinengründung, verkehrsinduzierte Schwingungen. Da der Boden sehr weit ausgedehnt ist, werden spezielle numerische Verfahren benötigt, um derartige Probleme numerisch lösen zu können. Eine solche Methode, die „Scaled Boundary Finite Element Method“, soll im Rahmen dieser Arbeit näher untersucht werden. Hierzu wird ein entsprechendes Matlab-Programm bereitgestellt, welches im Rahmen von umfangreichen Parameterstudien anzupassen und zu verwenden ist. Diese haben zum Ziel, Gültigkeitsgrenzen und Empfehlungen beispielsweise zur Zeitschrittwahl systematisch zu erarbeiten und entsprechend zusammenzufassen. Zur Verifikation sollen analytische Lösungen vereinfachter Wellenausbreitungsprobleme in unbegrenzten Gebieten sowie ggf. mit kommerzieller FE-Software erzeugte Vergleichslösungen herangezogen werden.

Contact: Tobias Kuhn, M.Sc., Carolin Birk, Prof. Dr.-Ing.

Master thesis: Phase field fracture modelling using the scaled boundary finite element method ("Schädigungsmodellierung mit der Phasenfeldmethode und SBFEM")

Failure of solids due to fracture is one of the prominent problems in engineering. A recent development in this direction is the phase field method which models the crack as a smeared continuum. This approach has an inherent characteristic of determining the crack path and branching, unlike other discrete crack modelling methodologies. This work includes understanding phase field modelling of fracture in the context of the scaled boundary finite element method and identifying the parameters that strongly influence the crack representation and propagation. Parameter studies are carried out on sample problems to evaluate the effect of each of these parameters.

[1] C. Miehe; F. Welschinger; M. Hofacker: Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations, International journal for Numerical Methods in Engineering, Vol. 83: 1273-1311, 2010
[2] Hirshikesh; A.L.N. Pramod; R.K. Annabattula; E.T. Ooi; C. Song; S. Natarajan: Adaptive phase-field modeling of brittle fracture using the scaled boundary finite element method, Computer Methods in Applied Mechanics and Engineering, Vol. 355:284-307, 2019

Contact: Ajay Kumar Pasupuleti, M.Sc.

Theses in progress

The following student projects and theses have already been assigned and are currently in progress.

• Automatisierte Übungstools für die Lehre in der Stabstatik
  Bachelor thesis – Supervision: Ajay Kumar Pasupuleti, M.Sc.

Completed theses

The following theses have already been completed.

• Implementation of Machine Learning to identify the parameters of a cohesive zone model for ductile fracture modelling
• Statische Berechnung einer hyperbolischen Paraboloidschale am Beispiel des "Teepotts" Warnemünde
• Vergleichsrechnung einer zweigleisigen Netzwerkbogenbrücke und einer Stabbogenbrücke ("A comparative study of tied arch bidges: network arch versus vertical hangers")
• Menscheninduzierte Schwingungen: Vergleichende Untersuchungen zur Lastmodellierung an Fußgängerbrücken ("Human-induced vibration of footbridges: a comparative study of load models")
• Implementation, validation and evaluation of a high-order implicit time-integration method for structural dynamics ("Implementierung, Validierung und Bewertung eines impliziten Zeitschrittverfahrens höherer Ordnung für die Strukturdynamik")
• Development of scaled boundary finite element method for heat conduction problems with convection boundary conditions ("Modellierung von Wärmeleitproblemen mit Konvektion mit der SBFEM")

• Vergleichende Untersuchung von Konstruktionsprinzipien für Schalentragwerke am Beispiel einer Gitterschale ("Structural principles: shell design vs. space frame – a comparative study")
• Smoothing techniques for image-based modelling of complex geometries in 3D using scaled boundary polyhedral elements
• Vergleich klassischer und moderner Verfahren zur statischen Berechnung am Beispiel des Sydney Opera House
• Untersuchungen zur Abschätzung von Lastmultiplikationsfaktoren für Stabilitätsnachweise von komplexen druck- und zugbeanspruchten Stabtragwerken
• Untersuchung der kombinierten Aussteifung von Gebäuden in Mischbauweise aus Stahlbeton und Mauerwerk im Erdbebenfall
• Physics-informed neural networks for computational mechanics
• Dynamische Analyse flüssigkeitsgefüllter Behälter
• Implementierung einer schubweichen Plattentheorie mittels der Finite-Elemente-Methode in Matlab
• Statische Berechnung einer hyperbolischen Paraboloidschale am Beispiel der Hyparschale Magdeburg
• Statische Berechnung und Aussteifungsberechnung eines Wohngebäudes mit Dachbegrünung
• Material parameter estimation by deep learning and wave-based techniques
• Towards phase field modelling using the scaled boundary finite element method
• Untersuchung zweier Systeme für den Lastfall Erdbeben

• Smoothing techniques for image-based modelling of microstructures using the scaled boundary finite element method
• Numerische Untersuchungen zum Einfluss der Boden-Bauwerk Interaktion auf die Dynamik von eingebetteten Rahmentragwerken
• Numerical investigation of resonance and trapping modes effects in plates with obstacles
• Implementation and comparative studies of time-domain solvers for nonlinear dynamics
• Development of a program for the automated evaluation of programming tasks in Python

• Enhancing the computation of finite element stiffness matrices by using neural networks
• Menscheninduzierte Schwingungen: Modellierung der Mensch-Bauwerk Interaktion
• Damage evaluation based on elastic guided waves facilitated by deep learning
• Image-based estimation of effective material properties by a deep learning approach

• Menscheninduzierte Schwingungen von Fußgängerbrücken: Fallstudie zur "Millenium Bridge"
• Finite element modeling of wave propagation problems
• Implementation of a higher-order finite element formulation for axisymmetric domains under non-axisymmetric loading
• Image-based seismic-site response analysis using the SBFEM

• Image-based computational homogenisation modelled by SBFEM
• Schwingungsmessung in der Baudynamik - Entwicklung eines mobilen experimentellen Labors
• Scaled boundary finite element analysis of thermal problems in cracked domains
• Polygon elements for stress analysis of functionally graded materials
• Transient thermal analysis using SBFEM for localised thermal effects
• Transient simulation of ultrasonic pulses propagating in coupled fluid-structure systems

• Image-based modelling of microstructures using the scaled boundary finite element method
• Untersuchung eines Bemessungskonzepts für Schwingungstilger anhand einer dynamischen Tragwerksanalyse für den Lastfall Erdbeben
• Development of polygon elements based on the scaled boundary finite element method