Abstract
This paper presents a new half-plane Michell structure that transmits a uniformly distributed load of infinite horizontal extent to a series of equally-spaced pinned supports. A full kinematic description of the structure is obtained for the case when the maximum allowable tensile stress is greater than or equal to the allowable compressive stress. Although formal proof of optimality of the solution presented is not yet available, the proposed analytical solution is supported by substantial numerical evidence, involving the solution of problems with in excess of 10 billion potential members. Furthermore, numerical solutions for various combinations of unequal allowable stresses suggest the existence of a family of related, simple, and practically relevant structures, which range in form from a Hemp-type arch with vertical hangers to a structure which strongly resembles a cable-stayed bridge.
Highlights
IntroductionThis is an extended version of a paper prepared by Pichugin et al (2011) for the 9th World Congress on Structural and Multidisciplinary Optimization, subsequently awarded the 2011 ISSMO/Springer Prize
Keywords Plastic design · Truss optimization · Michell structure · Uniformly distributed load. This is an extended version of a paper prepared by Pichugin et al (2011) for the 9th World Congress on Structural and Multidisciplinary Optimization, subsequently awarded the 2011 ISSMO/Springer Prize
We present a number of numerical solutions for similar problems with unequal allowable stresses, suggesting that a wider family of related, simple and practically relevant structures exists
Summary
This is an extended version of a paper prepared by Pichugin et al (2011) for the 9th World Congress on Structural and Multidisciplinary Optimization, subsequently awarded the 2011 ISSMO/Springer Prize. Electronic supplementary material The online version of this article (doi:10.1007/s00158-015-1278-0) contains supplementary material, which is available to authorized users In his groundbreaking contribution to the field of structural optimization, Michell (1904) formulated the sufficient conditions for a truss with equal tensile and compressive yield stresses to have the least volume. The problem involves a uniformly distributed vertical load applied along a horizontal line spanning across an infinite number of -spaced pinned supports The motivation for this configuration originates from the (still unsolved) classical problem of finding the optimal half-plane structure to transmit a uniformly distributed load along a line between two level pinned supports, to these supports, see Hemp (1974) and Chan (1975). In the case of equal allowable stresses and an infinite number of -spaced supports, the resulting geometry of the Michell structure, and the mathematical solution for kinematic fields, all turn out to be comparatively simple. We present a number of numerical solutions for similar problems with unequal allowable stresses, suggesting that a wider family of related, simple and practically relevant structures exists
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