PhD. course - Topology Optimization - Theory, Methods and Applications

June 19th - 25th 2019, Technical University of Denmark


Course Description:

The course will concentrate on theory and practice of topology design. Topics include:

•      Design parametrization (interpolation schemes, composites, etc.)

•      Sensitivity analysis (direct and adjoint methods)

•      Algorithms (OC-methods, mathematical programming, convex approximation schemes and other methods)

•      Computational issues (checkerboards, filters, robust design, parallelization)

•      Novel multiscale approaches

•      Applications in structural and multi-physics problems (industrial examples, MicroElectroMechanical Systems (MEMS), wave-propagation problems, additive manufacturing)

The course work includes study of preparatory reading material before course-start (see below).

An integral part of the course is computer exercises in Matlab and preparing a poster for presentation on the last day of the course; exercise work is planned for the weekend. Interested students may choose to perform part of the exercises based on the PETSc parallel computing platform.



All participants are required to bring a poster on the topic of their Ph.D. research work.




Ole Sigmund, Department of Mechanical Engineering, Technical University of Denmark

Jakob Søndergaard Jensen, Department of Mechanical Engineering, Technical University of Denmark

Casper Schousboe Andreasen, Department of Mechanical Engineering, Technical University of Denmark

Niels Aage, Department of Mechanical Engineering, Technical University of Denmark

Anton Evgrafov, Deparment of Mechanical Engineering, Technical University of Denmark



The course is designed for Ph.D.-students and final-year graduate students being familiar with the basic concepts of the finite element method. Knowledge corresponding to a course in FEM as well as Matlab experience is assumed. Students with advanced programming skills may work with the Python or C++ languages and/or the parallel computing platform TopOpt in PETSc.


Working Load:

Approximately 100 hours in total, including work during the June 19-25 course period at DTU (lectures, exercises, discussions, seminars) as well as preparatory required reading as well as poster preparation before course start.


Study Material

The course textbook is:

Martin P. Bendsøe and Ole Sigmund (2003 and 2004), "Topology Optimization: Theory, Methods and Applications."
Springer Verlag, 2003 or 2004, ISBN 3-540-42992-1.

Preparatory reading consists of Chapter 1 and Appendix 5.1.



All lectures will be given in English


Evaluation and Diplomas

To pass the course, active participation in all activities is required; this includes the exercises, the poster session, and the student presentations.

Grades: Pass/Fail.

ECTS points: 3.5


More about DTU and DCAMM

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