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A hybrid symmetry–PSO approach to finding the self-equilibrium configurations of prestressable pin-jointed assemblies

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Abstract

For pin-jointed assemblies with many members or self-stress states, the form-finding problem using conventional methods generally involves considerable computational complexities due to the large size of the solution spaces. Here, we propose an improved form-finding method for prestressable pin-jointed structures by combining symmetry-based qualitative analysis with particle swarm optimization. Expressed in the symmetry-adapted coordinate system, the nodal coordinate vectors of a structure with specific symmetry and topology are independently extracted from the key blocks of the small-sized force density matrices associated with rigid-body translations. Then, the first block of the equilibrium matrix is computed, in which the null space reveals integral self-stress states. Particle swarm optimization is introduced and adapted to find feasible prestress modes, where the uniformity and unilaterality conditions of the members are considered. Besides, the QR decomposition with column pivoting is adopted for efficient computations on the null space of these blocks. The QR decompositions of the small-sized blocks of the force density matrix and the equilibrium matrix are performed iteratively, to simultaneously find a stable self-equilibrium configuration and a feasible prestress mode. Representative examples show the presented method is computationally efficient and accurate for the form-finding of symmetric tensegrities and prestressed cable–strut structures.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Numbers 51508089 and 51850410513), Southeast University “Zhongying Young Scholars” Project, and the Fundamental Research Funds for the Central Universities. The first author would like to acknowledge financial support from the Alexander von Humboldt Foundation for his visiting research at Max-Planck-Institut für Eisenforschung GmbH, Germany. The last author would like to acknowledge the award of Research Fund for International Young Scientists from the National Natural Science Foundation of China. The authors are grateful to the editors and anonymous reviewers for their professional comments and valuable suggestions in improving the quality of the paper.

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Authors and Affiliations

  1. Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, and National Prestress Engineering Research Center, Southeast University, Nanjing, 211189, China

    Yao Chen, Jiayi Yan & Jian Feng

  2. Creative Design Engineering Lab (Cdel), School of Engineering, University of Liverpool, London Campus, London, UK

    Pooya Sareh

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  1. Yao Chen
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Correspondence to Yao Chen.

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Chen, Y., Yan, J., Feng, J. et al. A hybrid symmetry–PSO approach to finding the self-equilibrium configurations of prestressable pin-jointed assemblies. Acta Mech 231, 1485–1501 (2020). https://doi.org/10.1007/s00707-019-02586-6

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  • DOI: https://doi.org/10.1007/s00707-019-02586-6

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