Finding the strongest stable weightless column with a follower load and relocatable concentrated masses

Kirillov, Oleg and Overton, Michael (2020) Finding the strongest stable weightless column with a follower load and relocatable concentrated masses. The Quarterly Journal of Mechanics and Applied Mathematics. ISSN 0033-5614 (Submitted)

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Abstract

We consider a problem of optimal placement of concentrated masses along a weightless elastic column (rod) that is clamped at one end and loaded by a nonconservative follower force at the free end. The goal is to find the largest possible interval such that the variation in the loading parameter within this interval preserves stability of the structure. When the number of masses is two we find the optimal load analytically. For the case of three or more masses, we obtain conjectures for the globally optimal load that are strongly supported by extensive computational results. To obtain these, we use techniques from nonsmooth optimization, employing the recently developed open-source software package GRANSO (GRadient-based Algorithm for Non-Smooth Optimization) to maximize the load subject to appropriate non-smooth stability constraints.

Item Type: Article
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: John Coen
Date Deposited: 20 Aug 2020 09:53
Last Modified: 20 Aug 2020 10:00
URI: http://nrl.northumbria.ac.uk/id/eprint/44141

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