Document Type
Article
Publication Date
7-22-2009
Journal Title
SIAM Journal on Applied Mathematics
Volume Number
70
Issue Number
3
First Page
762
Last Page
788
DOI
https://doi.org/10.1137/090751608
Version
Publisher PDF: the final published version of the article, with professional formatting and typesetting
Disciplines
Mathematics
Abstract
In this work, we develop a finite trigonometric series representation for the stress in a multilayered Goupillaud-type elastic strip subjected to transient Heaviside loading on one end while the other end is held fixed. This representation is achieved by means of the z-transform method and involves the so-called base angles. Generally, different layered designs could share the same set of base angles, and the more layers the design has, the more base angles are expected. Necessary conditions for the base angles and design parameters for any given design are described. As a result of the stress representation, we are able to identify optimal layered designs which provide the smallest stress amplitude. For two- and three-layered designs, for which the coefficients of the stress representation are easy to find, the optimization results are achieved using a custom-made discrete optimization technique applied in [A. P. Velo and G. A. Gazonas, Int. J. Solids Structures, 40 (2003), pp. 6417–6428]. For other layered designs, the optimality conditions are predicted heuristically using pattern recognition and the necessary conditions for the base angles and design parameters. Applications of these optimization results include design improvement in making a nonoptimal design optimal. They are also extended to non-Goupillaud-type layered media with integer layer length ratios. Our results are supported by numerical experiments and provide means to validate numerical optimization codes.
Digital USD Citation
Velo, Ani P.; Gazonas, George A.; and Ameya, Takanobu, "Z-Transform Methods for the Optimal Design of One-Dimensional Layered Elastic Media" (2009). Mathematics: Faculty Scholarship. 4.
https://digital.sandiego.edu/mathematics-faculty/4
Notes
SIAM Journal on Applied Mathematics © 2009 Society for Industrial and Applied Mathematics
Original Citation: Velo, Ani & Gazonas, George & Ameya, Takanobu. (2010). Erratum: z-Transform Methods for the Optimal Design of One-Dimensional Layered Elastic Media.. SIAM Journal of Applied Mathematics. 70. 1736-1737. 10.1137/090773416.