Optimum structure for a uniform load over multiple spans

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 soluThis 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. Aleksey V. Pichugin [email protected] Andrew Tyas [email protected] Matthew Gilbert [email protected] Linwei He [email protected] 1 Department of Mathematics, CEDPS, Brunel University, Uxbridge UB8 3PH, UK 2 Department of Civil and Structural Engineering, University of Sheffield, Sheffield, S1 3JD, UK tions 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.