Efficient analysis of block circulant structures

Abstract

A circulant structures has a repetitive component and the entire structure can be formed through the rotation of the repetitive component about the axis of symmetry of the structure. The analysis of such structures can be simplified through the correct understanding of the circular properties. This paper introduces different types of circulant structures and determines the problem of their eigenvalues, which play a major role in engineering applications. Our study first introduces different types of circulant models that are not exclusively designed for simple domes, but rather they include many different types of structures such as power transmission towers, diamatic domes, pyramid domes, silos, etc. In circulant structures, an entire structure can be formed through rotation of the circulant component around the structural axis. A method for calculating the eigenvalues of a circulant structure is presented. In this method the circulant structural model is decomposed and the repetitive component of the structure is identified. This component, along with its connectivity with the previous and subsequent repetitive components, is modeled and the properties of the repetitive component are included in the computations. Examples are provided to show the efficiency of the circulant structural modeling and analysis, and the computational time for analysis of circulant structures is compared to those of the standard finite element program to demonstrate the efficiency of this type of modeling. The codes utilized in this study are written in MATLAB as provided in the Appendix.