A spline wavelet finite-element method in structural mechanics

• Published in: International journal for numerical methods in engineering 2006-04, Vol.66 (1), p.166-190
• Main Authors: Han, Jian-Gang, Ren, Wei-Xin, Huang, Yih
• Format: Article
• Language: English
• Subjects: Computational techniques; Exact sciences and technology; finite-element method; Fundamental areas of phenomenology (including applications); interpolation; Mathematical methods in physics; Physics; Solid mechanics; spline; Structural and continuum mechanics; structural mechanics; wavelet; wavelet finite-element method
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.1551

The wavelet‐based methods are powerful to analyse the field problems with changes in gradients and singularities due to the excellent multi‐resolution properties of wavelet functions. Wavelet‐based finite elements are often constructed in the wavelet space where field displacements are expressed as a product of wavelet functions and wavelet coefficients. When a complex structural problem is analysed, the interface between different elements and boundary conditions cannot be easily treated as in the case of conventional finite‐element methods (FEMs). A new wavelet‐based FEM in structural mechanics is proposed in the paper by using the spline wavelets, in which the formulation is developed in a similar way of conventional displacement‐based FEM. The spline wavelet functions are used as the element displacement interpolation functions and the shape functions are expressed by wavelets. The detailed formulations of typical spline wavelet elements such as plane beam element, in‐plane triangular element, in‐plane rectangular element, tetrahedral solid element, and hexahedral solid element are derived. The numerical examples have illustrated that the proposed spline wavelet finite‐element formulation achieves a high numerical accuracy and fast convergence rate. Copyright © 2005 John Wiley & Sons, Ltd.