Structural and Multidisciplinary Optimization

, Volume 57, Issue 3, pp 995–1003 | Cite as

Topological indentation pattern design of plates for maximum frequency gap

  • Niyazi Tanlak


The vibrational response of thin plates is improved by a new approach of indenting some portions along the normal direction so that the interval between two successive eigenfrequencies is enlarged while keeping their mass the same. Binary-coded genetic algorithm (GA) is used as the search algorithm. A stochastically-applied deterministic filter is developed like another genetic operator for GA to accelerate the convergence speed. The corresponding eigenfrequencies and their mode shapes are found by using finite element analysis. The results indicate significant improvement for the band-gap over no indentation designs and show the effectiveness of the new operator of GA.


Genetic algorithm New genetic operator Topology optimization Thin-walled structures Indentation pattern Frequency response Band gap 



Finite elements.


Finite element analysis.


Genetic algorithm.


Young’s modulus.

f(x, y)

Function defining the indentation pattern.


Plate thickness.

\( {N}_{i}^{e} \)

Total number of indented nodes in the neighborhood of element e, including itself.

\( {n}_{x,y,z}^{i} \)

x, y, z coordinates of i t h node in the admissible domain.


Constant probability.


Dynamic probability.



u, v, w

x, y, z displacements, respectively.


Total volume of the plate.


Vector form of displacements.

(xl, yl)

Lower bound.

(xu, yu)

Upper bound.

Gradient operator.

λ, μ

Lame’s constants.


Poisson’s ratio.




i t h resonance frequency.


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© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringBogazici University IstanbulBebekTurkey

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