Theoretical Foundations of Correct Wavelet-Based Approach to Local Static Analysis of Bernoulli Beam

Pavel A. Akimov; Mojtaba Aslami

doi:10.4028/www.scientific.net/AMM.580-583.2924

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 580-583Theoretical Foundations of Correct Wavelet-Based...

Theoretical Foundations of Correct Wavelet-Based Approach to Local Static Analysis of Bernoulli Beam

Abstract:

This paper is devoted to correct and efficient method of local static analysis of Bernoulli beam on elastic foundation. First of all, problem discretized by finite difference method, and then transformed to a localized one by using the Haar wavelets. Finally, imposing an optimal reduction in wavelet coefficients, the localized, reduced results can be obtained. It becomes clear after comparison with analytical solutions, that the localization of the problem by multiresolution wavelet approach gives exact solution in desired regions of beam even in high level of reduction in wavelet coefficients. This localization can be applied to any arbitrary region of the beam by choosing optimum reduction matrix and obtaining exact solutions with an acceptable reduced size of the problem.

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Periodical:

Applied Mechanics and Materials (Volumes 580-583)

Pages:

2924-2927

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.580-583.2924

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Online since:

July 2014

Authors:

Pavel A. Akimov*, Mojtaba Aslami

Keywords:

Averaging, Bernoulli Beam, Boundary Problem, Discrete Wavelet, Haar Basis, Local Structural Analysis, Reduced Wavelet Coefficients, Static Analysis, Wavelet-Based Methods

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References

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