Continuum sensitivity analysis and improved Nelson’s method for beam shape eigensensitivities

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Continuum sensitivity analysis and improved Nelson’s method for beam shape eigensensitivities

Giuseppe Maurizio Gagliardi, Mandar D. Kulkarni, Francesco Marulo

Abstract. Gradient-based optimization techniques require accurate and efficient sensitivity or design derivative analysis. In general, numerical sensitivity methods such as finite differences are easy to implement but imprecise and computationally inefficient. In contrast, analytical sensitivity methods are highly accurate and efficient. Although these methods have been widely evaluated for static problems or dynamic analysis in the time domain, no analytical sensitivity methods have been developed for eigenvalue problems. In this paper, two different analytical methods for shape eigensensitivity analysis have been evaluated: the Continuum Sensitivity Analysis (CSA) and an enhanced version of Nelson’s method. They are both analytical techniques but differ in how the analytical differentiation is performed: before and after the discretization, respectively. CSA has been applied to eigenvalue problems for the first time, while Nelson’s method has been improved and adapted to shape optimizations. Both methods have been applied to different cases involving shape optimization of beams. Both vibration and buckling problems were analysed considering the eigenvalue as a design variable. Both methods have been successfully applied, and Nelson’s method proved to be more convenient for this kind of problem.

Keywords
Continuum Sensitivity Analysis, Nelson’s Sensitivity Method, Gradient-Based Optimization Techniques, Shape Eigensensitivity

Published online 6/1/2024, 5 pages
Copyright © 2024 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: Giuseppe Maurizio Gagliardi, Mandar D. Kulkarni, Francesco Marulo, Continuum sensitivity analysis and improved Nelson’s method for beam shape eigensensitivities, Materials Research Proceedings, Vol. 42, pp 38-42, 2024

DOI: https://doi.org/10.21741/9781644903193-9

The article was published as article 9 of the book Aerospace Science and Engineering

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

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