Spannungsberechnung auf Basis von CT-Scans - Einzelansicht

The special project addresses the following four aspects: 

FFT method [single]:

The first student will be given an existing implementation of the FTT method and corresponding literature. The student will then

• Carry out a literature review
• analyze the computational complexity of the method analytically and for practical examples.
• analyze pros and cons of the method
• propose, rewrite and implement remedies 

Finite Cell Method (FCM) with Moment Fitting [single]:

The second student will be given an existing implementation of the moment fitting method for a 2D finite element case and corresponding literature. The student will then

• Carry out a short literature review
• Analyze the computational complexity of the method analytically
• Understand and implement the moment fitting method in FCM and analyze the computational complexity 

Pre-Integration [single]:

The third student will work on implementing a pre-integration technique. Additionally, the student will prepare a given FEM framework for a meaningful comparison of the homogenization methods of student one and two. The tasks include:

• Carry out a short literature review
• Analyze the computational complexity of the method analytically
• Implement the pre-integration method and analyze its computational complexity
• Prepare an interface to include the methods of student one and two.

[team]:

The three students will then jointly compare their results on benchmark examples in a written report and present their findings in a final presentation. The modified codes must be handed in along with the technical report.

For example:

[1] T. W. J. de Geus, J. Vondrejc, J. Zeman, R. H. J. Peerlings, und M. G. D. Geers, „Finite strain FFT-based non-linear solvers made simple”, Computer Methods in Applied Mechanics and Engineering, Bd. 318, S. 412–430, Mai 2017, doi: 10.1016/j.cma.2016.12.032.

[2] Yang, Z., „The Finite Cell Method for Geometry-Based Structural Simulation”, Dissertation, Technische Universität München, 2011. Verfügbar online: https://mediatum.ub.tum.de/1071102. Hubrich, S., & Düster, A., „Numerical integration for nonlinear problems of the finite cell an adaptive scheme based on moment fitting”, Computers & Mathematics with Applications, Bd. 77, Nr. 7, S. 1983-1997, 2019, doi: https://doi.org/10.1016/j.camwa.2018.11.030.

Time and place will be announced at the project fair.

Background Computational Mechanics

Programming knowledge (either C++ or Python)

Final presentation, code, and technical report.

M.Sc. Digital Engineering