This paper proposes a basic method for designing light and rigid structures that have a maximum natural frequency for a designated mode. A design variable “density,” related to the material properties of a three-dimensional solid element, is introduced into the finite element method (FEM). Thus, a structure is expressed as a density distribution inside its design domain, and the optimal structure is obtained by searching for the most suitable such distribution.

1.
Bendso̸e
M.
, and
Kikuchi
N.
,
1988
, “
Generating Optimal Topologies in Structural Design Using a Homogenization Method
,”
Computer Methods in Applied Mechanics and Engineering
, Vol.
71
, pp.
197
224
.
2.
Diaz
A. R.
, and
Kikuchi
N.
,
1992
, “
Solution to Shape and Topology Eigenvalue Optimization Problems Using a Homogenization Method
,”
International Journal for Numerical Methods in Engineering
, Vol.
35
, pp.
1487
1502
.
3.
Kingery, W. D., Bowen, H. K., and Uhlmann, D. R., 1960, Introduction to Ceramics, Johnson Wiley & Sons, Inc., New York, pp. 768–815.
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