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

Abstract:

High-accuracy solution of the problem of deep beam 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 deep beams 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.

• Periodical: Applied Mechanics and Materials (Volumes 405-408)
• Pages: 3165-3168
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.405-408.3165
• Online since: September 2013
• Authors: Pavel A. Akimov, Marina L. Mozgaleva
• Keywords: Analytical Solution, Averaging, Boundary Problem, Deep Beam Analysis, Discrete-Continual Methods, Haar Basis, Local Solution, Method of Extended Domain, Multilevel Methods, Structural Analysis, Wavelet-Based Methods

References

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