Efficient Optimum Design of Structures with Discrete Design Variables

Abstract

A method is presented for optimum design of structures, where some or all design variables can be chosen from a set of prescribed values. The main idea is to reduce the number of structural analyses in the process of optimization. First the structural responses such as forces and displacements are approximated as functions of cross-sectional properties, thus high quality explicit functions are generated for the responses. Employing these approximate expressions in the optimization process, the continuous optimum design can be achieved rapidly. Using the results obtained from the continuous variable optimization and with the help of the approximated responses, a branch and bound method is used to obtain the discrete design values. The results indicate that after the completion of the continuous variable optimization, only one or two extra detailed analyses of the structure is needed to complete the discrete variable optimization. In this work, a dome and a grillage are presented as test cases.

Get full access to this article

View all access options for this article.

References

Vanderplaats

G.N.

and Thanedar

P.B.

, A Survey of Discrete Variable Optimization for Structural Design, Proceedings of the Tenth ASCE Conference on Electronic Computation, ed. Ural

and Wang

T.L.

, American Society of Civil Engineers, New York, 1991, 173–180.

Olson

G.R.

and Vanderplaats

G.N.

, Method for Nonlinear Optimization with Discrete Design Variables, AIAA J., 27(11) (November 1989), 1584–1589.

Schmit

L.A.

and Fleury

, Discrete-Continuous Variables Structural Synthesis using Dual Methods, AIAA J., 18(12) (December 1980), 1515–1524.

Cameron

G.E.

, Xu

and Grierson

D.E.

, Discrete Optimal Design of 3D Frameworks, Proceedings of the Tenth ASCE Conference on Electronic Computation, ed. Ural

and Wang

T.L.

, American Society of Civil Engineers, New York, 1991, 181–188.

Balling

R.J.

, Optimal Steel Frame Design by Simulated Annealing, J. of Structural Engineering, ASCE, 117(6) (June 1991), 1780–1795.

Templeman

A.B.

, Discrete Optimum Structural Design, Computers and Structures, 30(3) (1988), 511–518.

Vanderplaats

G.N.

, Numerical Optimization Techniques for Engineering Design: With Applications, McGraw-Hill, Inc., New York, 1984.

Schmit

L.A.

and Miura

, Approximation Concepts for Efficient Structural Synthesis, NASA CR 2552 (March 1976).

Lust

R.V.

and Schmit

L.A.

, Alternative Approximation Concepts for Space Frame Synthesis, NASA CR (March 1985).

10.

Yoshida

and Vanderplaats

G.N.

, Structural Optimization Using Beam Elements, AIAA J., 24(4), (April 1988), 454–462.

11.

Salajegheh

and Vanderplaats

G.N.

, An Efficient Approximation Method for Structural Synthesis With Reference To Space Structures, International Journal of Space Structures 2(3) (1986/87), 165–175.

12.

Vanderplaats

G.N.

and Salajegheh

, a New Approximation Method for Stress Constraints in Structural Synthesis, AIAA J., 27(3) (1989), 352–358.

13.

Vanderplaats

G.N.

and Salajegheh

, An Efficient Approximation Technique for Frequency Constraints in Frame Optimization, International Journal for Numerical Methods in Engineering, 26(1988), 1057–1069.

14.

Vanderplaats

G.N.

, Thomas

H.L.

and Shyy

Y.K.

, A Review of Approximation Concepts for Structural Synthesis, Computing Systems in Engineering, 2(1) (1991), 17–25.

15.

Shin

D.K.

, Gurdal

and Griffin

O.H.

, A Penalty Approach for Nonlinear Optimization with Discrete Design Variables, Engineering Optimization, 6(1990), 29–42.

16.

Sepulvida

A.E.

, Jin

I.M.

and Schmit

L.A.

, Optimal Placement of Active Elements in Control Augmented Structural Synthesis, AIAA Paper No. 92–2557-CP, AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Dallas, TX, April 13–15, 1992, 2768–2787.

17.

DOT User's Manual, VMA Engineering, Goleta, CA (1989).

18.

DOC User's Manual, VMA Engineering, Goleta, CA (1991).

19.

Vanderplaats

G.N.

and Moses

, Structural Optimization by Method of Feasible Directions, Computer and Structures, 3 (1973), 739–755.