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...
متن کاملThe Shape of the Tallest Column: Corrected
Our summary of the work of Keller and Niordson (J. Math. Mech. 16, pp. 433–446, 1966) was inaccurate. We offer a correction.
متن کاملThe Tallest Column — A Dynamical System Approach Using a Symmetry Solution
A classic problem, the design of the tallest column, is solved again using a different method. By the use of a similarity solution the equations are transformed and the difficult singularity at the endpoint is peeled away. The resulting autonomous system has a critical point and the solution must be on its stable manifold. The solution is found by starting near the critical point in the directi...
متن کاملOptimality conditions in convex optimization revisited
The phrase convex optimization refers to the minimization of a convex function over a convex set. However the feasible convex set need not be always described by convex inequalities. In this article we consider a convex feasible set which are described by inequality constraints which are locally Lipschitz and not necessarily convex and need not be smooth. We show that if the Slater’s constraint...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1999
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(98)00188-5