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unilogo University of Stuttgart
Institute of Engineering and Computational Mechanics

Model Reduction of Mechanical Systems


Lecture Model Reduction of Mechanical Systems

Summer term
Jun.-Prof. Dr.-Ing. Jörg Fehr

Lecture Content

Nowadays, the use of lighter structures demands for the consideration of elastic effects for many components. Mostly, the modeling and numerical simulation of elastic bodies is achieved with the finite element method, which often leads to a high number of degrees of freedom, more than a million degrees of freedom is not unusual. Therefore, one essential step for an efficient simulation is the reduction of the elastic degrees of freedom. The complex model is replaced with a far simpler one, which still accurately captures the most important aspects of the phenomena being modeled.
This course presents the basic mathematical theory for projection-based model reduction. The lecture is accompanied by exercises, mainly practical Matlab programming exercises.

Course Outline:

Introduction / mathematical basics for model reduction / error analysis / modal reduction techniques / basics from control theory / reduction of second order MIMO systems / Krylov-based model reduction / methods based on Gramian matrices / Proper Orthogonal Decomposition / numerical methods used for model reduction / model reduction of large scale systems (excursion to the HLRS) / SVDMOR / nonlinear model reduction of mechanical systems / current research topics in model reduction of mechanical systems (parametric approaches)

Lecture Information

  • Audience:
    The lecture is intended for students in their Msc programme as well as SimTech students.
  • Extent: 3 credit points (2 SWS)
  • Lecture:
    • Tuesday, 8:00 a.m. to 9:30 a.m., V7.04
    • The lectures begins on Tuesday, April 18th, 2017
  • Excercises: The lecture is accompanied by exercises, mainly practical Matlab programming exercises. It is allowed to work on them in groups of 2 to 3 students. Please upload only one solution per group to ILIAS.
  • Exam: A written exam is planned but depending on the amount of participants it could be substituted in favor of an oral exam.
  • All material can be found on ILIAS.
Modern High Performance Cluster at the HLRS.
Convergence behavior of a Krylov subspace reduction approach.
FE crash model of a Ford Taurus with 2.7 million degrees of freedom for model reduction.