| Summary: | 碩士 === 國立成功大學 === 機械工程學系碩博士班 === 91 === The objective of this dissertation is to study the construction of the wavelet-finite element method. In traditional finite element methods, polynomials are used as interpolation functions to construct an element; the degrees of freedom are restricted by the order of polynomial. When the problem with local high gradient is analyzed by using traditional finite element methods, the higher order polynomial or denser mesh must be employed to ensure the accuracy.
In the wavelet-finite element method, wavelet functions are employed as interpolation functions and wavelet coefficients are employed as the degrees of freedom. We must construct the space transform matrix to transform wavelet coefficients to nodal displacements and rotations, because elements are constructed in wavelet space. By using the transform matrix, neighboring elements can be connected and processing boundary conditions can be processed directly.
Daubechies scaling functions possess elegant properties of orthonormal, compact support and time-frequency localization. The wavelet-element is introduced into the finite element procedure and the dynamic problems of a bar structure. The accuracy and the convergence rate are verified. Then same dynamic problems of a beam structure are solved by the present wavelet-element modal.
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