TECHNICAL NOTES
Aug 1, 1986

Interpreting Adjoint Equations in Structural Optimization

Publication: Journal of Structural Engineering
Volume 112, Issue 8

Abstract

The adjoint method has been used in structural optimization to compute sensitivity coefficients of cost and constraint functions with respect to design parameters. The adjoint method involves the calculation of an adjoint vector from certain adjoint equations. So far, the adjoint equations have been considered only as a numerical tool for computing sensitivity coefficients. In this paper, the adjoint equations are given a physical interpretation, and it is shown that the components of the adjoint vector are the influence coefficients associated with the given function. Importantly, the interpretation of adjoint equations in this paper provides a new method for obtaining influence coefficients.

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References

1.
Arora, J. S., and Haug, E. J., “Methods of Design Sensitivity Analysis in Structural Optimization,” AIAA Journal, Vol. 17, No. 19, 1979, pp. 970–974.
2.
Carlton, T. M., “Principle of Virtual Work in Relation to Muller‐Breslau's Principle,” International Journal of Mechanical Science, Vol. 22, No. 8, 1980, pp. 523–525.
3.
Fleming, J. F., and Shah, A. P., “Truss Influence Lines on a Time Sharing System,” Computers and Structures, Vol. 4, No. 5, Oct., 1974, pp. 933–950.
4.
Haug, E. J., and Arora, J. S., Applied Optimal Design, John Wiley & Sons, N. Y., 1979.
5.
Norris, C. H., and Wilbur, J. B., Elementary Structural Analysis, McGraw‐Hill, N. Y., 1960.
6.
Vanderplaats, G. N., “Comment on Methods of Design Sensitivity Analysis in Structural Optimization,” AIAA Journal, Vol. 18, No. 11, 1980, pp. 1406–1408.

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Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 112Issue 8August 1986
Pages: 1971 - 1976

History

Published online: Aug 1, 1986
Published in print: Aug 1986

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Ashok D. Belegundu, A. M. ASCE
Asst. Prof., Dept. of Mech. Engrg., The Pennsylvania State Univ., University Park, PA 16802

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