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Published in:
Definitions from Graph Theory and Graph Products Read chapter Read first chapter

2020 | OriginalPaper | Chapter

2. Basic Concepts and Definitions of Symmetry and Regularity

Authors : Ali Kaveh, Hossein Rahami, Iman Shojaei

Published in: Swift Analysis of Civil Engineering Structures Using Graph Theory Methods

Publisher: Springer International Publishing

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Abstract

Concepts and definitions for different types of symmetry and regularity are already published in a book by Kaveh, “Optimal Analysis of Structures by Concepts of Symmetry and Regularity”. In this chapter definitions and concepts relevant to the contents of the present book are provided to make it self-content. In this chapter different types of graph products, method of block diagonaliztion, techniques of calculating the eigenvalues and eigenvectors, decomposition of adjacency and Laplacian, and circulant matrices are presented.

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previous chapter Definitions from Graph Theory and Graph Products
next chapter Static Analysis of Near-Regular Skeletal Structures: Additional Members
Literature
1.
Kaveh, A.: Optimal Analysis of Structures by Concepts of Symmetry and Regularity. Springer, GmbH, Wien-NewYork (2013). ISBN 978-3-7091-1564-7CrossRef
2.
Kaveh, A., Rahami, H.: Compound matrix block diagonalization for efficient solution of eigenproblems in structural mechanics. Acta Mech. 188(3–4), 155–166 (2007)CrossRef
3.
Kaveh, A., Rahami, H.: Special decompositions for eigenproblems in structural mechanics. Commun. Numer. Methods Eng. 22(9), 943–953 (2006)MathSciNetCrossRef
4.
Kaveh, A., Rahami, H.: An efficient method for decomposition of regular structures using graph products. Int. J. Numer. Methods Eng. 61, 1797–1808 (2004)MathSciNetCrossRef
5.
Kaveh, A.: Structural Mechanics: Graph and Matrix Methods, 3rd edn. Research Studies Press (John Wiley), UK (2006)MATH
6.
Kaveh, A., Rahami, H.: Block diagonalization of adjacency and Laplacian matrices for graph product; applications in structural mechanics. Int. J. Numer. Methods Eng. 68(1), 33–63 (2006)MathSciNetCrossRef
7.
Kaveh, A., Rahami, H.: An efficient analysis of repetitive structures generated by graph products. Int. J. Numer. Methods Eng. 84(10), 108–126 (2010)MathSciNetCrossRef
8.
Kaveh, A., Rahami, H.: Block circulant matrices and applications in free vibration analysis of cyclically repetitive structures. Acta Mech. 217(1–2), 51–62 (2011)CrossRef
Metadata
Title
Basic Concepts and Definitions of Symmetry and Regularity
Authors
Ali Kaveh
Hossein Rahami
Iman Shojaei
Copyright Year
2020
Book
Swift Analysis of Civil Engineering Structures Using Graph Theory Methods

Print ISBN: 978-3-030-45548-4

Electronic ISBN: 978-3-030-45549-1

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-45549-1_2

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