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Nonlinear form-finding of symmetric cable–strut structures using stiffness submatrices associated with full symmetry subspace

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Abstract

An efficient and nonlinear form-finding method is proposed for symmetric cable–strut structures with complex geometry or many nodes. Expressed in the symmetry-adapted coordinate system, the first block matrix of the symmetry-adapted tangent stiffness matrix is extracted using the full symmetry subspace, which is much smaller-sized and associated with the first irreducible representation of a symmetry group. Then, this stiffness submatrix and the principle of minimum potential energy are adopted for the fast but stable convergence of the initial configuration to the stable configuration. During the form-finding process, the generalized inverse of a matrix and modification for the minimum eigenvalues are employed, to guarantee the positive definiteness of the stiffness submatrix. The form-finding process can start from an arbitrary initial configuration, whereas only certain symmetry group, and the connectivity pattern and the initial lengths of the members should be given in advance. A few numerical examples are illustrated to show the efficiency and accuracy of the form-finding method for cable–strut structures with complex geometry and different symmetry.

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Acknowledgements

This work has been supported by the National Natural Science Foundation of China (Grant Nos. 51978150 and 51850410513) 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 authors are grateful to the anonymous reviewers for their valuable comments.

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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

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  1. Yao Chen
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  2. Jiayi Yan
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  3. Jian Feng
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Correspondence to Yao Chen.

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Chen, Y., Yan, J. & Feng, J. Nonlinear form-finding of symmetric cable–strut structures using stiffness submatrices associated with full symmetry subspace. Arch Appl Mech 90, 1783–1794 (2020). https://doi.org/10.1007/s00419-020-01696-1

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