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Michell-like 2D layouts generated by genetic ESO

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Abstract

The theory of least-weight trusses for one load condition and a stress constraint was established by Michell (Philos Mag 8:589–597, 1904). His work was largely ignored for about 50 years, but from then on, a lot of research effort has been devoted to construct optimal topologies satisfying Michell’s optimality criteria. But the exact analytical Michell layout is still not known for most boundary conditions. It is therefore useful to develop numerical methods for generating approximate Michell-like topologies. We show in this paper that genetic ESO (GESO) methods are suitable for constructing Michell-like layouts. To illustrate the validity of GESO, seven different load cases for a plane structure with two point supports are considered. The Michell-like layouts are generated for vertical or horizontal loads applied at different heights and different angles. The results are compared and classified and a new Michell truss is proposed on the basis of the GESO results. Plane structures under two point loads are also considered, and the GESO results are compared with Melchers (Struct Multidisc Optim 29:85–92, 2005) solutions.

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Acknowledgements

[Acknowledgement] The authors are indebted to National Science Foundation of China (Project No. 50908082) for financial support.

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  1. College of Civil Engineering, Hunan University, Changsha, Hunan, China

    Xia Liu & Wei-Jian Yi

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  1. Xia Liu
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  2. Wei-Jian Yi
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Correspondence to Xia Liu.

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Liu, X., Yi, WJ. Michell-like 2D layouts generated by genetic ESO. Struct Multidisc Optim 42, 111–123 (2010). https://doi.org/10.1007/s00158-009-0474-1

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