An efficient method for decomposition of regular structures using graph products

2004 ◽  
Vol 61 (11) ◽  
pp. 1797-1808 ◽  
Author(s):  
A. Kaveh ◽  
H. Rahami
Keyword(s):  
Efficient Method ◽  
Graph Products ◽  
Regular Structures

An efficient method for seismic analysis of structures

2015 ◽  
Vol 32 (6) ◽  
pp. 1708-1721 ◽  
Author(s):  
A. Kaveh ◽  
H. Rahami ◽  
Iman Shojaei
Keyword(s):  
Finite Difference ◽  
Dynamic Analysis ◽  
Modal Analysis ◽  
Efficient Method ◽  
Seismic Analysis ◽  
Boundary Value ◽  
Efficient Solutions ◽  
Matrix Inversion ◽  
Graph Products ◽  
Content Type

Purpose – The purpose of this paper is to present an efficient method for dynamic analysis of structures utilizing a modal analysis with the main purpose of decreasing the computational complexity of the problem. In traditional methods, the solution of initial-value problems (IVPs) using numerical methods like finite difference method leads to step by step and time-consuming recursive solutions. Design/methodology/approach – The present method is based on converting the IVP into boundary-value problems (BVPs) and utilizing the features of the latter problems in efficient solution of the former ones. Finite difference formulation of BVPs leads to matrices with repetitive tri-diagonal and block tri-diagonal patterns wherein the eigensolution and matrix inversion are obtained using graph products rules. To get advantage of these efficient solutions for IVPs like the dynamic analysis of single DOF systems, IVPs are converted to boundary-value ones using mathematical manipulations. The obtained formulation is then generalized to the multi DOF systems by utilizing modal analysis. Findings – Applying the method to the modal analysis leads to a simple and efficient formulation. The laborious matrix inversion and eigensolution operations, of computational complexities of O(n2.373) and O(n3), respectively, are converted to a closed-form formulation with summation operations. Research limitations/implications – No limitation. Practical implications – Swift analysis has become possible. Originality/value – Suitability of solving IVPs and modal analysis using conversion and graph product rules is presented and applied to efficient seismic optimal analysis and preliminary design.

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