A topological optimization technique using the conception of OMD (Optimal Material Distribution) is presented for free vibration problems of a structure. A new objective function corresponding to multieigenvalue optimization is suggested for improving the solution of the eigenvalue optimization problem. An improved optimization algorithm is then applied to solve these problems, which is derived by the authors using a new convex generalized-linearization approach via a shift parameter which corresponds to the Lagrange multiplier and the use of the dual method. Finally, three example applications are given to substantiate the feasibility of the approaches presented in this paper.

Issue Section:
Technical Papers
Topics:
Free vibrations, Optimization, Eigenvalues, Optimization algorithms
1.
Bendso̸e
M. P.
, and
Kikuchi
N.
,
1988
, “
Generating Optimal Topologies in Structural Design Using a Homogenization Method
,”
Comput. Methods Appl. Mech. Energ.
, Vol.
71
, pp.
197
–
24
.
2.
Bendso̸e
M. P.
,
1989
, “
Optimal Shape Design as a Material Distribution Problem
,”
Structural Optimization
, Vol.
1
, pp.
193
–
202
.
3.
Diaz, A., and Kikuchi, N., 1992, “Solution to Shape and Topology Eigenvalue Optimization Problems Using a Homogenization Method,” International Journal for Numerical Methods in Engineering, to appear.
4.
Fleury
C.
, and
Braibant
V.
,
1986
, “
Structural Optimization: A New Dual Method Using Mixed Variables
,”
International Journal for Numerical Methods in Engineering
, Vol.
23
, pp.
409
–
428
.
5.
Fleury
C.
,
1989
, “
Efficient Approximation Concepts Using Second Order Information
,”
International Journal for Numerical Methods in Engineering
, Vol.
28
, pp.
2041
–
2058
.
6.
Haftka
R. T.
, and
Grandhi
R. V.
,
1986
, “
Structural Shape Optimization—A Survey
,”
Comput. Methods Appl. Mech. Energ.
, Vol.
57
, pp.
91
–
106
.
7.
Haftka, R. T., and Gurdal, Z., 1992, “Elements of Structural Optimization,” 3rd rev. and expanded ed., Kluwer Academic Publishers, The Netherlands, pp. 283–318.
8.
Ma
Z.-D.
, and
Hagiwara
I.
,
1991
a, “
Sensitivity Analysis Methods for Coupled Acoustic-Structural Systems, Part 1: Modal Sensitivities
,”
AIAA Journal
, Vol.
29
, No.
11
, pp.
1787
–
1795
.
1.
Ma
Z.-D.
, and
Hagiwara
I.
,
1991
b, “
Development of New Mode-Superposition Technique for Truncating the Lower and/or Higher Frequency Modes, 3rd Report, An Application of Eigenmode Sensitivity Analysis Method for Systems with Repeated Eigenvalues
,”
Transactions of the JSME
, Vol.
57
, No.
536C
, pp.
1156
–
1163
(in Japanese);
2.
JSME International Journal, Series C
, Vol.
37
, No.
1
, pp.
14
–
20
.
1.
Ma
Z.-D.
,
Kikuchi
N.
, and
Hagiwara
I.
,
1992
, “
Structural Topoiogy/Shape Optimization for a Frequency Response Problem
,”
Computational Mechanics
, Vol.
13
, No.
3
, pp.
157
–
174
.
2.
Olhoff, N., 1981, “Optimization of Transversely Vibrating and Rotating Shafts,” Optimization of Distributed Parameter Structures, E. J. Haug and J. Cea, eds., Sijthoff and Noordhoff, pp. 177–199.
3.
Olhoff
N.
, and
Taylor
J. E.
,
1983
, “
On Structural Optimization
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
50
, pp.
1134
–
1151
.
4.
Olhoff
N.
,
Bendso̸e
M.
, and
Rasmussen
J.
,
1991
, “
On CAD-Integrated Structural Topology and Design Optimization
,”
Comput. Methods Appl. Mech. Energ.
, Vol.
89
, pp.
259
–
279
.
5.
Suzuki, K., and Kikuchi, N., 1990, “Generalized Layout Optimization of Shape and Topology in Three-Dimensional Shell Structures,” Rept. No. 90-05, Dept. Mich. Engrg. and Appl. Mech., Comp. Mech. Lab., University of Michigan, USA.
6.
Suzuki
K.
, and
Kikuchi
N.
,
1991
, “
A Homogenization Method for Shape and Topology Optimization
,”
Comput. Methods Appl. Mech. Energ.
, Vol.
93
, pp.
291
–
318
.
7.
Svanberg
K.
,
1987
, “
The Method of Moving Asymptotes—A New Method for Structural Optimization
,”
International Journal for Numerical Methods in Engineering
, Vol.
24
, pp.
359
–
373
.
This content is only available via PDF.
Copyright © 1995
 by The American Society of Mechanical Engineers
You do not currently have access to this content.