Wavelet Method For Solving Differential Equations On Elastic Mechanics

With the development of computer technology and the requirements of practical application, all the problems arising in science and engineering field are closed related with computers. Due to the high rank of the differential equations in elastic mechanics and the difficulties of finding accurate solutions for these equations, the numerical solutions to these equations are especially important in engineering. As a powerful tool of numerical analysis, wavelet analysis was developed from 1970s and has been widely used to solve differential equations and integral equations. This thesis is focused on the research of wavelet methods to solve differential equations in elastic mechanics and a series of results are obtained. It is divided into 3 chapters and the main ideas of each chapter are as follows:In Chapter 1, some general knowledge of wavelet analysis and basic theories of elastic mechanics are briefly discussed, the current applications of wavelet analysis in differential equations are investigated, and the feasibility of using orthogonal wavelets to solve differential equations is also proposed.In Chapter 2, the wavelet method for solving problems of beams on elastic groundsill is investigated, and four aspects are illustrated: differential control equation of a beam on Winkler groundsill; the definition and property and integral operational matrix of the linear Legendre multi-wavelet; the numerical solutions to the differential control equation of a beam on Winkler groundsill solved by linear Legendre multi-wavelet; numerical examples.In Chapter 3. the wavelet solutions to problems of laminas on elastic groundsill is researched and is divided into five sections: differential control equation of a plate on the two-parameter elastic groundsill; the definition and differential operational matrix of the Sine-Cosine wavelet: the construction of the two-dimensional Sine-Cosine wavelet using tensor product and two differential operational matrices; the numerical solutions to the differential equation of a rectangular plate on the two-parameter elastic groundsill solved by two-dimensional Sine-Cosine wavelet; numerical example.