A sensitivity interpretation of adjoint variables in optimal design

Ashok D. Belegundu, Jasbir S. Arora

    Research output: Contribution to journalArticle

    14 Citations (Scopus)

    Abstract

    The adjoint method of computing derivatives of cost and constraint functions with respect to design variables requires the calculation of certain adjoint variables. Until now, the adjoint variables have been looked upon only as some intermediate vectors needed to calculate design derivatives. In this paper, they are shown to have an important significance. They represent the sensitivity of the cost and constraint functions with respect to the loading or forcing function in the design problem. A sensitivity theorem for the adjoint variables is presented for structural, mechanical dynamic, and distributed parameter systems. These results offer some immediate practical advantages, such as a method for computing influence coefficients for structural systems, and a method for verifying (debugging) the analytical calculation of adjoint variables in development of a computer code.

    Original languageEnglish (US)
    Pages (from-to)81-89
    Number of pages9
    JournalComputer Methods in Applied Mechanics and Engineering
    Volume48
    Issue number1
    DOIs
    StatePublished - Jan 1 1985

    Fingerprint

    sensitivity
    Derivatives
    influence coefficient
    distributed parameter systems
    Costs
    costs
    checkout
    theorems
    Optimal design
    computer programs

    All Science Journal Classification (ASJC) codes

    • Computational Mechanics
    • Mechanics of Materials
    • Mechanical Engineering
    • Physics and Astronomy(all)
    • Computer Science Applications

    Cite this

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    abstract = "The adjoint method of computing derivatives of cost and constraint functions with respect to design variables requires the calculation of certain adjoint variables. Until now, the adjoint variables have been looked upon only as some intermediate vectors needed to calculate design derivatives. In this paper, they are shown to have an important significance. They represent the sensitivity of the cost and constraint functions with respect to the loading or forcing function in the design problem. A sensitivity theorem for the adjoint variables is presented for structural, mechanical dynamic, and distributed parameter systems. These results offer some immediate practical advantages, such as a method for computing influence coefficients for structural systems, and a method for verifying (debugging) the analytical calculation of adjoint variables in development of a computer code.",
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    A sensitivity interpretation of adjoint variables in optimal design. / Belegundu, Ashok D.; Arora, Jasbir S.

    In: Computer Methods in Applied Mechanics and Engineering, Vol. 48, No. 1, 01.01.1985, p. 81-89.

    Research output: Contribution to journalArticle

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