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Uniform loading problems for periodic domains: examples of optimal structures

Uniform loading problems for periodic domains: examples of optimal structures
A. V. Pichugin1, A. Tyas2 and M. Gilbert2
1 Dept. of Mathematical Sciences, Brunel University, Uxbridge, UK
2 Dept. of Civil and Structural Engineering, University of Sheffield, UK

Structures that can transmit a uniform vertical load to one or several level pinned supports represent a useful, even if simplified, metaphor for a number of important engineering problems. Unfortunately, the corresponding optimal structures are usually highly non-trivial. Even with the additional simplifying assumption that the structure is an optimal truss in the limit (plastic) design, i.e. a Michell structure, only a handful of relevant examples have been described in the literature. All of the classical examples of such structures featured one or two supports; however, we recently showed that the extension to an infinite horizontal line of equally spaced supports (or, equivalently, to a horizontally-periodic optimization domain), significantly simplifies the problem, especially in the case when maximum allowable tensile stress is greater or equal than the allowable compressive stress. In this presentation we will describe in some detail the analytical derivation of the Michell structure that solves this problem and demonstrate how the modern tools for discrete layout optimisation motivated the derivation. We will also present a number of structures, obtained numerically, for the case when the allowable tensile stress is lower than the allowable compressive stress. These results will demonstrate a surprising and non-trivial relationship between two common types of bridge designs and also suggest the likely layout for the periodic structure obtained in the limit when the allowable tensile stress is much lower than the allowable compressive stress.

References
Pichugin, A. V., Tyas, A. and Gilbert, M. (2011) Michell structure for a uniform load over multiple spans, in Proceedings of the Ninth World Congress on Structural and Multidisciplinary Optimization (WCSMO-9), Shizuoka, Japan.
Pichugin, A. V., Tyas, A. and Gilbert, M. (2012) On the optimality of Hemp's arch with vertical hangers, Structural and Multidisciplinary Optimization, 46(1), pp. 17–25, doi:10.1007/s00158-012-0769-5.

 

   
© Realizacja Zbigniew Kacprzyk