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The goal of this project was the optimization of a floor component of a actual Opel passenger car. The project was operated in cooperation with Adam Opel AG. The optimization goal was the improvement of dynamic behavior in order to improve the acoustic properties of the component.

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Model data: Opel XXX Bodengruppe, Ausgangsmodell

Model format: NASTRAN

mechanically equivalent supported car body substructure

Number of FE-nodes: 113.000

Number of FE-elements: 106.000

Spot weld formulation by RBE3 with central Hexa element



Eigenfrequency analysis:

The analysis results show a very low value of only 22Hz for the first eigenfrequency. This is undesired because it may yield to resonance effects with external excitations. The goal of the shape optimization was to find a bead structure that provides a significant improvement of the first eigenfrequency (>70Hz).

Opel XXX Bodengruppe, Frequenzanalyse, Mode 1

Eigenmode 1, Eigenfrequency: 22,1Hz

Opel XXX Bodengruppe, Frequenzanalyse, Mode 2

Eigenmode 2, Eigenfrequency 30,8Hz

Opel XXX Bodengruppe, Frequenzanalyse, Mode 3

Eigenmode 3, Eigenfrequency 43,9Hz

Opel XXX Bodengruppe, Frequenzanalyse, Mode 4 Eigenmode 4, Eigenfrequency 56,7Hz


Optimization modelOpel XXX Bodengruppe, Designraum

The figure on the right hand side shows the design domain for the bead optimization. It spans over the central blank which is the most important component for the investigated eigenfrequencies. The optimization variables are defined by the surface normals of all FE-nodes in the design domain. They are highlighted by the red color. This definition results in an optimization problem with 7500 variables.

Optimization parameter:

  • objective: maximize the four smallest eigenfrequencies
  • constraints:  maximum bead height 10mm
  • filter radius: 40mm
  • full mesh regularization


Optimization resultOpel XXX Bodengruppe, optimiertes Modell

The optimal bead geometry for the given constraints is depicted in the figure on the right hand side. The beads are scaled with a factor of 2.5 for better visibility. The optimal bead geometry allows for an effective stiffening of the blank and a tremendous improvement of the relevant eigenfrequencies.

  • 1. eigenfrequency: original: 22,1Hz      optimal: 94,0Hz
  • 2. eigenfrequency: original: 30,8Hz      optimal: 110,9Hz
  • 3. eigenfrequency: original: 43,9Hz      optimal: 125,0Hz
  • 4. eigenfrequency: original: 56,7Hz      optimal: 132,7Hz


The optimized bead geometry shows an explicit structure that is easy to interpret. The optimal shape is reflected by a FE-mesh with high quality without serious element deformations. This ensure reliable analysis results without numerical stiffening effects.



This application example shows the potential of thin metal sheet components with optimal bead structures. Due to the complexity of the designs and decreasing development times such optimal bead designs cannot be found by pure experience or trial and error approaches. The numerical shape optimization with FE-based parametrization is the best tool to develop such efficient bead structures by an completely automatically procedure. Supported by this results the design engineer is able to construct a very efficient bead structure in a very small amount of time without the necessity of time consuming parameter studies.