Next Article in Journal
Towards Real-Time Facial Landmark Detection in Depth Data Using Auxiliary Information
Previous Article in Journal
Harmonic Principles of Elemental Crystals—From Atomic Interaction to Fundamental Symmetry
Article Menu
Issue 6 (June) cover image

Export Article

Open AccessReview
Symmetry 2018, 10(6), 229; https://doi.org/10.3390/sym10060229

Group-Theoretic Exploitations of Symmetry in Novel Prestressed Structures

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.
Received: 10 May 2018 / Revised: 12 June 2018 / Accepted: 15 June 2018 / Published: 15 June 2018
Full-Text   |   PDF [3132 KB, uploaded 17 June 2018]   |  

Abstract

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
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Chen, Y.; Feng, J. Group-Theoretic Exploitations of Symmetry in Novel Prestressed Structures. Symmetry 2018, 10, 229.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top