Deslauriers–Dubuc interpolating wavelet beam finite element

• Published in: Finite elements in analysis and design Vol. 75; pp. 71 - 77
• Main Authors: Burgos, Rodrigo Bird, Cetale Santos, Marco Antonio, Silva, Raul Rosas e
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.11.2013
• Subjects: Axisymmetric cylindrical shell; Beam on elastic foundation; Beams (radiation); Daubechies wavelet; Derivatives; Deslauriers–Dubuc interpolating wavelet; Finite element method; Interpolet; Joints; Mathematical analysis; Mathematical models; Vectors (mathematics); Wavelet; Wavelet-based beam element; Daubechies wavelet; Wavelet-based beam element; Beam on elastic foundation; Axisymmetric cylindrical shell; Deslauriers–Dubuc interpolating wavelet; Interpolet
• ISSN: 0168-874X; 1872-6925
• DOI: 10.1016/j.finel.2013.07.004

This paper presents the formulation of beam finite elements based on Deslauriers–Dubuc interpolating wavelets, also known as Interpolets. Unlike other wavelet families like Daubechies, Interpolets possess rational filter coefficients, are smooth, symmetric and therefore more suitable for use in numerical methods. Displacement and rotation shape functions are obtained and presented graphically. Expressions for stiffness matrix and force vector are developed based on connection coefficients, which are inner products of basis functions and their derivatives. In order to validate the formulation, several examples with increasing level of complexity are tested and results are compared with analytical and standard beam element solutions. •A beam finite element based on Deslauriers–Dubuc interpolating wavelets (Interpolets) is formulated.•Some properties of Interpolets are presented (rational filter coefficients, smoothness and symmetry).•Expressions for derivatives and connection coefficients are developed.•Interpolet-based shape functions are obtained and presented graphically. Expressions for stiffness matrix and force vector are derived.•Several examples with increasing level of complexity are successfully tested and results compared with analytical and standard beam element solutions.