Wavelet Analysis has called the attentions in numerical solutions of PDEs in recent years. Because of orthogonality and compact support of Daubechies scaling functions, these functions have excellent ability of providing good accuracy and convergence for the approximation of the solution in singularities. In this article the method of using these functions for numerical solving of PDE for Euler–Bernoulli beams is formulated. This procedure needs to calculate derivatives and integrals of scaling functions as the shape functions of wavelet-based finite element method. Because of non-explicit formulation and high oscillation of these functions, conventional methods -like Gauss method for integration- are not suitable and accurate. Thus some special methods are formulated for these requirements. The ability and high accuracy of wavelet-based beam element for different boundary conditions and loads is shown in some examples.
Naraghi, S. E., & Noorzad, A. (2011). Formulation of Beam Element for Wavelet-Based Finite Element Method. Journal of Civil and Surveying Engineering, 45(5), 611-622.
MLA
S. E. Naraghi; A. Noorzad. "Formulation of Beam Element for Wavelet-Based Finite Element Method". Journal of Civil and Surveying Engineering, 45, 5, 2011, 611-622.
HARVARD
Naraghi, S. E., Noorzad, A. (2011). 'Formulation of Beam Element for Wavelet-Based Finite Element Method', Journal of Civil and Surveying Engineering, 45(5), pp. 611-622.
VANCOUVER
Naraghi, S. E., Noorzad, A. Formulation of Beam Element for Wavelet-Based Finite Element Method. Journal of Civil and Surveying Engineering, 2011; 45(5): 611-622.
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