Müller-Breslau's Principle in Adjoint Design Sensitivity Analysis

Research output: Contribution to journalArticle

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Abstract

The adjoint variable method is now a well-known approach for calculating design sensitivity coefficients in structural systems. The adjoint variable method has its origins in optimal control theory. For structures, however, the adjoint variables have important significance. Past results have shown the adjoint displacements to be sensitivity coefficients with respect to the load vector. For linear functions, the adjoint displacements have been shown to be influence coefficients associated with the function, an important finding in locating worstcase positions of moving loads in bridge design. In this paper, further interpretations are presented. Specifically, the adjoint load is interpreted physically and is shown to be an initial strain and/or initial displacement given to the structure. This fact, together with previous findings, has been related to the classical Müller-Breslau principle in mechanics. Finally, a proof of equivalence is provided between the aforementioned adjoint variable method derived from optimal control theory and the adjoint-structure approach published recently. This equivalence is also evident from the adjoint load interpretations given in the paper.

Original languageEnglish (US)
Pages (from-to)333-347
Number of pages15
JournalMechanics of Structures and Machines
Volume17
Issue number3
DOIs
StatePublished - Sep 1 1989

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Design Sensitivity Analysis
sensitivity analysis
Control theory
Sensitivity analysis
Adjoint Variable Method
Sensitivity Coefficient
Mechanics
Optimal Control Theory
control theory
Equivalence
optimal control
Design Sensitivity
Moving Load
equivalence
influence coefficient
Linear Function
sensitivity
coefficients
Coefficient

All Science Journal Classification (ASJC) codes

  • Engineering(all)

Cite this

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abstract = "The adjoint variable method is now a well-known approach for calculating design sensitivity coefficients in structural systems. The adjoint variable method has its origins in optimal control theory. For structures, however, the adjoint variables have important significance. Past results have shown the adjoint displacements to be sensitivity coefficients with respect to the load vector. For linear functions, the adjoint displacements have been shown to be influence coefficients associated with the function, an important finding in locating worstcase positions of moving loads in bridge design. In this paper, further interpretations are presented. Specifically, the adjoint load is interpreted physically and is shown to be an initial strain and/or initial displacement given to the structure. This fact, together with previous findings, has been related to the classical M{\"u}ller-Breslau principle in mechanics. Finally, a proof of equivalence is provided between the aforementioned adjoint variable method derived from optimal control theory and the adjoint-structure approach published recently. This equivalence is also evident from the adjoint load interpretations given in the paper.",
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Müller-Breslau's Principle in Adjoint Design Sensitivity Analysis. / Belegundu, A. D.

In: Mechanics of Structures and Machines, Vol. 17, No. 3, 01.09.1989, p. 333-347.

Research output: Contribution to journalArticle

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