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: Variational (Energy) Physics-Informed Neural Networks for 2-D Linear Elasticity
("Variationsbasierte (Energie-) Physik-informierte Neuronale Netze für die 2D-lineare Elastizität")

Physics-informed neural networks (PINNs) are state-of-the-art ML models designed using ANNs that embed physical laws into neural-network training to solve partial differential equations (PDEs). Here, two main categories exist: (i) strong-form PINNs, which penalize pointwise PDE residuals, and (ii) variational (energy) PINNs, which minimize a weak/energy functional via numerical quadrature. While strong-form PINNs are simple to set up, variational PINNs can reduce the required derivative order and often show improved stability for mechanics problems. In this work, a ready-to-use strong-form PINN code for 2-D linear elasticity is provided. The main objective is to design and implement a variational PINN for a 2-D boundary value problem (BVP), and perform a detailed, reproducible comparison against the strong-form baseline and the analytical solution.

[1] T. Rashid: Make your own neural network. CreateSpace Independent Publishing Platform, 2016.
[2] E. Haghighat, M. Raissi, A. Moure, H. Gomez, R. Juanes: A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics. CMAME 379:113741, 2021.
[3] E. Kharazmi, Z. Zhang, G. E. Karniadakis: Variational Physics-Informed Neural Networks for Solving Partial Differential Equations. arXiv:1912.00873, 2019.

Contact: Dipraj Kadlag, M.Sc.

Master thesis: Comparison of Fracture Modeling Techniques: Discrete Approaches and Phase-Field Simulations ("Vergleich von Bruchmodellierungstechniken: Diskrete Ansätze und Phasen-Feld-Simulationen")

Failure in solids due to fracture is a prominent problem in engineering. Fracture simulation requires in-depth understanding of available discrete fracture models and numerical techniques to solve these complex problems. In addition, it is necessary to solve the problem on a mesh that is fine enough to represent stress singularities, necessitating systematic studies. In this work, discrete fracture theories and related finite element technology are elaborated in detail, and fracture simulations are performed using commercial software (Ansys). Obtained results are then compared with the phase-field fracture model, thus helping in obtaining insights about different fracture modeling techniques.

Contact: Ajay Kumar Pasupuleti, M.Sc.

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.

Master thesis: High-performance computing using a parallel explicit solver for elasto-dynamic problems ("Hochleistungsrechnen mit einem parallelen expliziten Löser für elasto-dynamische Probleme")

Dynamic loading resulting from various physical processes—such as earthquakes and impacts—is ubiquitous in engineering practice. Analytical solutions to such transient problems are generally unavailable; therefore, structural responses are approximated using numerical methods, such as the explicit central difference method [1]. By lumping the mass matrix, nodal displacements can be evaluated without solving the system of linear equations. When the computational domain is spatially discretized using Octree meshes [2] and numerically represented by scaled boundary finite elements, computational efficiency is further enhanced by parallelizing the explicit solver [3]. In this work, the proposed parallelization will be implemented in MATLAB. The implementation will be validated, and a cost analysis study will be carried out to measure the effectiveness of the parallelization.

[1] A.K. Chopra: Dynamics of Structures – Theory and Application to Earthquake Engineering, Pearson Education, Inc., ISBN: 978-0-13-285803-8.
[2] A. Saputra; H Talebi; D Tran; C Birk; and C Song: Automatic image-based stress analysis by the scaled boundary finite element method, International Journal for Numerical Methods in Engineering, Vol. 109:697–738, 2017.
[3] J. Zhang; A. Ankit; H. Gravenkamp; S. Eisenträger; and C. Song: A massively parallel explicit solver for elasto-dynamic problems exploiting octree meshes, Computer Methods in Applied Mechanical Engineering, Vol. 380: 113811, 2021.

Contact: Sharath Nattoji-Shara, M.Sc.

Theses in progress

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

Completed theses

The following theses have already been completed.

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

• Development of a software tool for structural analysis of plane frames based on the displacement method
• Automatisierte Übungstools für die Lehre in der Stabstatik

• 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