**Multiscale Wavelet Finite Element Analysis in Structural Dynamics** Multiscale Wavelet Finite Element Analysis

DOI: 10.5772/intechopen.71882

Mutinda Musuva and Cristinel Mares

in Structural Dynamics

Additional information is available at the end of the chapter Mutinda Musuva and Cristinel Mares Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.71882

### Abstract

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Science and Technology. 2001;**17**:355-365

Over the recent past, various numerical analysis techniques have been formulated and used to obtain approximate solutions for numerous engineering problems to aid predict the behaviour of systems accurately and efficiently. One such approach is the Wavelet Finite Element Method (WFEM) which involves combining the classical Finite Element Method (FEM) with wavelet analysis. The key desirable properties exhibited by some wavelet families, such as compact support, multiresolution analysis (MRA), smoothness, vanishing moments and the 'two-scale' relations, make the use of wavelets in WFEM advantageous, particularly in the analysis of problems with strong nonlinearities, singularities and material property variations present. The wavelet based finite elements (WFEs) of a rod and beam are formulated using the Daubechies and B-spline wavelet on the interval (BSWI) wavelet scaling functions as interpolating functions due to their desirable properties, thus making it possible to alter the local scale of the WFE without changing the initial model mesh. Specific benchmark cases are presented to exhibit and compare the performance of the WFEM with FEM in static, dynamic, eigenvalue and moving load transient response analysis for homogenous systems and functionally graded materials, where the material properties continuously vary spatially with respect to the constituent materials.

Keywords: multiresolution, wavelets, wavelet finite element (WFE), eigenvalue analysis, moving load problem, functionally graded material (FGM)
