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Zbl 1202.74083
Kaveh, A.; Rahami, H.
An efficient analysis of repetitive structures generated by graph products. (English)
[J] Int. J. Numer. Methods Eng. 84, No. 1, 108-126 (2010). ISSN 0029-5981

Summary: In this paper, an efficient method is developed for the analysis of regular structures. A structure is called regular if its model can be formed by a graph product. Here, instead of direct solution of the equations corresponding to a regular structure or finding the inverse of the stiffness matrix directly, modal analysis is used, and eigenvectors are employed for calculating the displacements and then internal forces of the structures. For this purpose, first an efficient method is developed for calculating the eigenvectors of the product graphs, and then a method is presented for using these eigenvectors for evaluating the displacements of a structure.

MSC 2000:: *74H99 Dynamical problems
05C90 Appl. of graph theory

Keywords: regular structures; analysis; graph products; Cartesian product; strong Cartesian product; direct product; lexicographic product

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