Buckling of bar by wavelet galerkin method

Abstract

Wavelet are used in data compression, signal analysis and image processing and also for analyzing non stationary time series. Wavelets are the functions which satisfy certain mathematics requirements and are used in other functions. The use of wavelets in mechanics can be viewed from two perspectives, first the analysis of mechanical response for extraction of modal parameters, damage measures, de-noising etc and second the solution of the differential equations governing the mechanical system. Wavelet theory provides various basis functions and multi-resolution methods for finite element method. Wavelet-based beam element can be constructed by using Daubechies scaling functions as an interpolating function. In the present thesis, the compactly supported Daubechies wavelet based numerical solution of boundary value problem has been presented for the instability analysis of prismatic members. This problem can be discretized by the Wavelet-Galerkin method. The evaluation of connection coefficients plays an important role in applying wavelet galerkin method to solve partial differential equations. The buckling problem of axially compressed bars by using Wavelet-Galerkin method is explained in this thesis. The comparisons are made with analytical solutions and with finite element results. The present investigation indicated that wavelet technique provides a powerful alternative to the finite element method.
The thesis has been presented in six number of chapters. Chapter 1 deals with the general introduction to wavelets and different types of wavelet families and their properties. The review of literature confining to the scope of study has been presented in chapter 2. The Chapter 3 deals with the properties of Daubechies wavelets and determination of scaling function, wavelet function, filter coefficients and moments of scaling function for different order of Daubechies wavelets. The computation of connection coefficients are described in Chapter 4. Chapter 5 deals with the Wavelet Galerkin method and the buckling problem of prismatic bar by using wavelet Galerkin method. It also includes the numerical results obtained from the present work, and comparisons made with analytical solutions and with finite element results. The Chapter6 concludes the present investigation. An account of possible scope of extended study has been presented to the concluding remarks. At last, some important publications and books referred during the present investigation have been listed in Reference section.
KEYWORDS: Introduction to wavelet theory, Daubechies wavelets scaling function, connection coefficients, wavelet galerkin method, buckling of bars.