Wavelet-Based Multilevel Discrete-Continual Finite Element Method for Local Plate Analysis

Pavel A. Akimov; Marina L. Mozgaleva

doi:10.4028/www.scientific.net/AMM.351-352.13

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 351-352Wavelet-Based Multilevel Discrete-Continual Finite...

Wavelet-Based Multilevel Discrete-Continual Finite Element Method for Local Plate Analysis

Abstract:

High-accuracy solution of the problem of plate analysis is normally required in some pre-known domains (regions with the risk of significant stresses that could potentially lead to the destruction of structure, regions which are subject to specific operational requirements). The distinctive paper is devoted to correct wavelet-based multilevel discrete-continual finite element method for local analysis of plates with regular (in particular, constant or piecewise constant) physical and geometrical parameters (properties) in one direction. Initial discrete-continual operational formulation of the considering problem and corresponding operational formulation with the use of wavelet basis are presented. Due to special algorithms of averaging within multigrid approach, reduction of the problem is provided. Resultant multipoint boundary problem of structural mechanics for system of ordinary differential equations with piecewise-constant coefficients is given.

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Periodical:

Applied Mechanics and Materials (Volumes 351-352)

Pages:

13-16

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.351-352.13

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Online since:

August 2013

Authors:

Pavel A. Akimov*, Marina L. Mozgaleva

Keywords:

Analytical Solution, Averaging, Boundary Problem, Discrete-Continual Method, Haar Basis, Local Solution, Method of Extended Domain, Multilevel Method, Plate Analysis, Structural Analysis, Wavelet-Based Method

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References

[1] Akimov P.A.: Correct Discrete-Continual Finite Element Method of Structural Analysis Based on Precise Analytical Solutions of Resulting Multipoint Boundary Problems for Systems of Ordinary Differential Equations. / Applied Mechanics and Materials Vols. 204-208 (2012).

DOI: 10.4028/www.scientific.net/amm.204-208.4502

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[2] Akimov P.A., Mozgaleva M.L.: Correct Wavelet-based Multilevel Numerical Method of Local Solution of Boundary Problems of Structural Analysis. / Applied Mechanics and Materials Vols. 166-169 (2012), pp.3155-3158.

DOI: 10.4028/www.scientific.net/amm.166-169.3155

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[3] Akimov P.A., Sidorov V.N.: Correct Method of Analytical Solution of Multipoint Boundary Problems of Structural Analysis for Systems of Ordinary Differential Equations with Piecewise Constant Coefficients. / Advanced Materials Research Vols. 250-253, 2011, pp.3652-3655.

DOI: 10.4028/www.scientific.net/amr.250-253.3652

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