The tallest column problem: New first integrals and estimates
نویسندگان
چکیده
منابع مشابه
The tallest column — optimality revisited
The problem of the optimal design of the tallest unloaded column under selfweight is revisited with a view towards clarifying the optimality of the design proposed by Keller and Niordson (The Tallest Column, J. Math. Mech. 16 (1966), pp. 433–446). The height of the tallest column is related to the rst eigenvalue of a Sturm–Liouville operator. Since the operator associated with the Keller–Niords...
متن کاملThe Shape of the Tallest Column∗
The height at which an unloaded column will buckle under its own weight is the fourth root of the least eigenvalue of a certain Sturm–Liouville operator. We show that the operator associated with the column proposed by Keller and Niordson [J. Math. Mech., 16 (1966), pp. 433– 446] does not possess a discrete spectrum. This calls into question their formal use of perturbation theory, so we consid...
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Our summary of the work of Keller and Niordson (J. Math. Mech. 16, pp. 433–446, 1966) was inaccurate. We offer a correction.
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ژورنال
عنوان ژورنال: Comptes Rendus Mécanique
سال: 2019
ISSN: 1631-0721
DOI: 10.1016/j.crme.2019.09.001