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Group-Theoretic Exploitations of Symmetry in Novel Prestressed Structures

by Yao Chen and Jian Feng *
Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, and National Prestress Engineering Research Center, Southeast University, Nanjing 211189, China
Author to whom correspondence should be addressed.
Symmetry 2018, 10(6), 229;
Received: 10 May 2018 / Revised: 12 June 2018 / Accepted: 15 June 2018 / Published: 15 June 2018
In recent years, group theory has been gradually adopted for computational problems of solid and structural mechanics. This paper reviews the advances made in the application of group theory in areas such as stability, form-finding, natural vibration and bifurcation of novel prestressed structures. As initial prestress plays an important role in prestressed structures, its contribution to structural stiffness has been considered. General group-theoretic approaches for several problems are presented, where certain stiffness matrices and equilibrium matrices are expressed in symmetry-adapted coordinate system and block-diagonalized neatly. Illustrative examples on structural stability analysis, force-finding analysis, and generalized eigenvalue analysis on cable domes and cable-strut structures are drawn from recent studies by the authors. It shows how group theory, through symmetry spaces for irreducible representations and matrix decompositions, enables remarkable simplifications and reductions in the computational effort to be achieved. More importantly, before any numerical computations are performed, group theory allows valuable and effective insights on the behavior or intrinsic properties of a prestressed structure to be gained. View Full-Text
Keywords: symmetry; cable-strut structures; structural stability; form-finding; bifurcation analysis symmetry; cable-strut structures; structural stability; form-finding; bifurcation analysis
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Chen, Y.; Feng, J. Group-Theoretic Exploitations of Symmetry in Novel Prestressed Structures. Symmetry 2018, 10, 229.

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