Abstract
For given allowable stress, Michell (Ref. 1) has investigated the optimal design of a cantilever truss that is to transmit a given load to two given fixed points of support. Disregarding the weight of the connections between the bars, he found that the truss of minimum weight is a truss-like continuum with an infinity of joints, and with bars that are mostly of infinitesimal length. In the present paper, a finite number of joints is enforced by including in the structural weight, which is to be minimized, not only the weight of the bars but also the weight of their connections, which is assumed to be proportional to the number of joints. The concept of two adjoint trusses is introduced, each of which coincides with the Maxwell diagram of the other truss. Two adjoint trusses have the same weight, and an optimal truss is therefore self-adjoint. The optimal configurations of 6-joint and 11-joint cantilever trusses are discussed, and the range of the weight of the typical joint is determined for which the 6-joint truss is optimal.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Michell, A. G. M.,The Limits of Economy in Frame-Structures, Philosophical Magazine, Series 6, Vol. 8, pp. 589–597, 1904.
Prager, W.,A Note on Discretized Michell Structures, Computer Methods in Applied Mechanics and Engineering, Vol. 3, pp. 349–355, 1974.
Parkes, E. W.,Joints in Optimum Frameworks, International Journal of Solids and Structures, Vol. 11, pp. 1017–1022, 1975.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Prager, W. Optimal layout of cantilever trusses. J Optim Theory Appl 23, 111–117 (1977). https://doi.org/10.1007/BF00932301
Issue Date:
DOI: https://doi.org/10.1007/BF00932301