A multinode superelement in the generalized strain formulation

Koen Dwarshuis*, Marcel Ellenbroek, Ronald Aarts, Dannis Brouwer

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)
55 Downloads (Pure)


Design and optimization of flexure mechanisms and real time high bandwidth control of flexure based mechanisms require efficient but accurate models. The flexures can be modeled using sophisticated beam elements that are implemented in the generalized strain formulation. However, complex shaped frame parts of the flexure mechanisms could not be modeled in this formulation. The generalized strain formulation for flexible multibody analysis defines the configuration of elements using a combination of absolute nodal coordinates and deformation modes.
This paper defines a multinode superelement in this formulation, i.e., an element having its properties derived from a reduced linear finite element model. This is accomplished by defining a local element frame with the coordinates depending on the absolute nodal coordinates. The linear elastic deformation is defined with respect to this frame, where rotational displacements are defined using the off-diagonal terms of local rotation matrices. The element frame can be defined in multiple ways; the most accurate results are obtained if the resulting elastic rotations are as small as possible. The inertia is defined in two different ways: the so-called "full approach" gives more accurate results than the so-called "corotational approach" but requires a special term that is not available from standard finite element models. Simulations show that (flexure based) mechanisms can be modeled accurately using smart combinations of superelements and beam elements.
Original languageEnglish
Pages (from-to)367-399
Number of pages33
JournalMultibody system dynamics
Early online date7 Nov 2022
Publication statusPublished - Dec 2022


  • Model order reduction
  • Flexible multibody dynamics
  • Component mode synthesis
  • Floating frame of reference formulation
  • Absolute nodal coordinate formulation
  • Corotational formulation
  • UT-Hybrid-D


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