Total Solution for Structural Optimization

case study 01 : The Shape Optimization of A Car Brake Part


Natural Frequency is one of the important indicators to express the vibration characteristic of the machine structure.
In the development of various products, it is demanded to find the shape whose natural frequency accords with the desired value efficiently.
For example, ...

  • The case that it evades resonance at specific frequency.
  • The case to make the FEM model which has the natural frequency same as the experimental value, etc.

This is an example of the shape optimization to synchronize a lot of natural frequencies of car brakes.

Analysis Model

Car Brake Part


  • Scale : About 160*135*85 [mm]
  • Element Type : Second-Order Tetrahedral Element
  • Number of Elements : 15,922
  • Number of Nodes : 29,352
  • Constraint Condition in Frequency Response Analysis Solver : none
  • Frequency Response Analysis Solver : Block Lanczos Solver

Optimization Condition

For the 7th to the 21th eigenmodes, OPTISHAPE-TS changes the shape and makes those natural frequencies agree with the target values in the following conditions as keeping the initial volume.

  • Optimization Method : Nonparametric Shape Optimization
  • Object : Volume (Dummy) *1
  • Constraint : as follows
Constraint Func. Constraint value
(compared with initial shape)
Constraint Func. Constraint value
(compared with initial shape)
mode 7
110.3% Eigenvalue
mode 15
mode 8
104.8% Eigenvalue
mode 16
mode 9
91.0% Eigenvalue
mode 17
mode 10
82.5% Eigenvalue
mode 18
mode 11
99.2% Eigenvalue
mode 19
mode 12
83.1% Eigenvalue
mode 20
mode 13
94.3% Eigenvalue
mode 21
mode 14
106.5% Volume * 100.0%

* It is necessary for OPTISHAPE-TS to set at least one objective function. Here, it is set a volume in both objective/constraint functions not to change a volume. The minimization of the volume isn't carried out because constraint function is given priority to, in the process of the optimization.

Shape Constraint : The red part of the shape below doesn't change.

  • Shape Constraint 1
  • Shape Constraint 2


Objective/Constraint Function Graph It got the result shape which each eigenvalue and the volume agreed with each specified value. (Precision : Error of 0.001% or less)

  • Time : 23 min
  • The optimization repetition : 10 times
    [ Natural Frequency Analysis : 28 times a step ]
  • OS : RedHat Linux
  • CPU : Core2Quad 2.66GHz
  • Memory : 1,200[MB]
  • Result Shape
    Result Shape
  • Cross-Section


Compare the initial shape and result shape, the cange of shape is comparatively calm though the eigenvalue is different about 20% at the maximum.

In the existing software of the parametric optimization, there is the case that result shape is unrealistic, or doesn't reach the targeted eigenvalue.
However, Nonparametric Shape Optimization changes surface shape freely without setting design parameters, so it can get the realistic shape which eigenvalue satisfies the demand..

Nonparametric Shape Optimization of OPTISHAPE-TS, adopts algorithm based on Smoothing Gradient Method (Traction Method) and can deal with a lot of limitation conditions efficiently. In this case study, you can see the optimization is efficiently going well by the change of values of objective/constraint functions while the convergence.

And, in this case ,it set control of the eigenvalue by initial shape ratio appointment, but can set it by modulus appointment or more, too.

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