Topology Optimization

(Topologische Strukturoptimierung)

Lecturer: Prof. Nicolas R. Gauger, Lisa Kusch
Date and Place:
Thursdays, 15:30h – 17:00h, SC Seminar Room 32-349, Lecture/Exercise
Wednesdays, 08:15h – 9:45h, SC Seminar Room 32-349, Lecture/Exercise
Note: First lecture will be on 26.11.2014. Exercises start shortly after that date.
ECTS: 4.5
Language: German or English
Link to lecture in KIS
Link to OLAT course


Master students in mathematics and computer science. Preferably with some basic knowledge about PDEs and numerics.

Source: S. Schmidt

Source: S. Schmidt


While questioning specific structural design problems, the students learn how to model and compute structures (e.g. bridges, components, micro structures) and their characteristics (e.g. compliance) and how to set up discrete models for the structural design. The final goal is to enable the students to treat topology optimization problems for structures, while the methods for topology optimization make also use of sizing and shape design methodologies (as in case of bubble methods). In tutorials based on MATLAB and open source software, the students will get hands on the derived methods for topology optimization. The lecture is furthermore valuable for general lectures on optimization with PDEs. For those students who have heard already lectures on optimization with PDEs, the lecture gives a specific problem and application oriented insight into this class of optimization problems.


  • Linear elastic equations and its discretization
  • Sizing optimization
  • Shape optimization
  • Topology optimization
  • Material distribution problems
  • Optimal microstructures
  • Bubble method
  • Derivation and characteristics of topological gradients