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Isoperimetric Inequalities in Mechanics

Friday, April 13, 10AM – 11AM
ACE 6.304

Robert Lipton

B. De Saint-Venant proposed in 1856 that among all prismatic shafts with a given cross-sectional area the greatest torsional rigidity is obtained by a shaft with circular cross section. We revisit this problem and address it for imperfectly bonded fiber reinforced shafts.

For a fixed area fraction of fiber cross-sections we seek to find the best combination of shaft cross-section, fiber shapes and fiber configurations that give the greatest torsional rigidity. We discuss these questions using simple calculus arguments and the notion of rearrangement inequalities. We illustrate the interplay between the 1st nonzero Stekloff eigenvalue of each fiber cross-section and the degree of imperfect bonding and its effect on the selection of the the most rigid fiber reinforced shaft configuration.

The talk will be Friday, April 13, at 10 am in the ICES 6th floor seminar room (ACES 6.304). Coffee and cookies will be provided. We hope to see you there.

Hosted by Ivo Babuska