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Analytic solutions of elastically supported Michell trusses

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Abstract

In this short note, analytic solutions of elastically supported Michell truss with varying support stiffness and support positions are presented. They are obtained by using the solution for the three forces problem in Michell truss theory and the compatibility condition at the elastic support. The developed solutions are in good agreement with numerical solutions from Sokół’s 99 line code for the optimization of discretized Michell truss with the support force in analytic solution. Besides, optimality criteria and a numerical example for minimum compliance design of elastically supported truss are discussed; both of them show the minimum compliance designs of elastically supported truss subject to proper material volume constraint are also a Michell truss and in good agreement with our analytic solutions.

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Acknowledgments

This work is supported by National Natural Science Foundation of China (91216201).

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Authors and Affiliations

  1. State Key Lab for Structural Analysis of Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, China

    Fei Niu & Gengdong Cheng

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  1. Fei Niu
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  2. Gengdong Cheng
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Correspondence to Fei Niu.

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Niu, F., Cheng, G. Analytic solutions of elastically supported Michell trusses. Struct Multidisc Optim 49, 689–694 (2014). https://doi.org/10.1007/s00158-013-0998-2

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