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Article
Publication date: 17 July 2009

Latif Ebrahimnejad and Reza Attarnejad

The purpose of this paper is to introduce a novel approach to solving linear systems arising from applying a Boundary Element Method (BEM) to elasticity problems.

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Abstract

Purpose

The purpose of this paper is to introduce a novel approach to solving linear systems arising from applying a Boundary Element Method (BEM) to elasticity problems.

Design/methodology/approach

The key idea is based on using wavelet transforms as a tool to change dense and fully populated matrices of BEM systems into sparse matrices. Wavelets are then used again to produce an algorithm to solve the resultant sparse linear systems. The wavelet transformation part of the method can be added as a black box to existing BEM codes.

Findings

Numerical results focusing on the sensitivity of the solution for various physical variables to the thresholding parameters, and savings in computer time and memory are presented. The results show that the proposed method is efficient for large problems.

Research limitations/implications

Application of the proposed method is restricted to problems with number of DOF equal to an integer power of 2.

Originality/value

The novel algorithm to solve transformed algebraic linear equations uses NS‐form of the modified matrix, taking the advantage of the hierarchical nature of Multi‐Resolution Analysis (MRA) to decompose a parent system into descendant systems with reduced size. These smaller systems are then solved iteratively using generalized minimal residual method.

Details

Engineering Computations, vol. 26 no. 5
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 24 August 2010

Reza Attarnejad

Purpose — Analysis of nonprismatic members has received a great deal attention from designers and engineers due to their ability in satisfaction of architectural and aesthetic…

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Abstract

Purpose — Analysis of nonprismatic members has received a great deal attention from designers and engineers due to their ability in satisfaction of architectural and aesthetic necessities. Using these structural members in complex structures such as aircrafts, turbine blades and space vehicles, exact static and dynamic analyses of these members become more significant. Based on structural/mechanical principles, the purpose of this paper is to present a new method to evaluate exact structural matrices for nonprismatic Euler‐Bernoulli beam elements. Design/methodology/approach — Through introducing the concept of basic displacement functions (BDFs), it is shown that exact shape functions are derived in terms of BDFs. BDFs and their derivatives have structural interpretations; therefore, they are obtained via application of flexibility method. Unlike the conventional methods, which are almost categorized as displacement‐based methods, the flexibility basis of the method ensures the true satisfaction of equilibrium equations at any interior point of the element. Findings — The exact shape functions and consequently structural matrices are derived for general nonprismatic beam elements. Numerical examples are carried out to determine static deflection and natural frequencies, and the results are highly competent with the other methods in literature. Research limitations/implications — The method can be extended to structural analysis of curved beams, plates and shells as well. Moreover, it is possible to derive exact dynamic shape functions via BDFs by solving the governing equation for transverse vibration of beams. Theoretically, the method faces limitation in analysis of nonprismatic beams that converge to a point where cross‐sectional area and moment of inertia are equal to zero. Practical implications — The development of this idea, i.e. BDFs seems to lead to promotive novel approaches for structural analysis and could be a breaking point for developing new elements for plates and shells as it was shown for beam elements. Originality/value — The paper's introduction of special functions, namely BDFs and their application, in both static and dynamic analyses of structures, could be a breaking point in analysis procedures.

Details

Engineering Computations, vol. 27 no. 6
Type: Research Article
ISSN: 0264-4401

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