Wavelet Finite Element Theory and Its Engineering Applications

Author: He Zhengjia
Publisher:
Publish Date: 2006-04-01
Features: This book discusses the fundamental theory of wavelet finite elements, introduces wavelet multi-resolution analysis, and presents the basic properties of Daubechies wavelets, interval B-spline wavelets, and second-generation wavelets. It explores the essence of wavelet multi-resolution analysis for the layer-by-layer nested approximation of the finite element solution space, constructing a series of one-dimensional and two-dimensional Daubechies wavelet, interval B-spline wavelet, and second-generation wavelet finite element units. The wavelet finite element method is applied to theoretical and experimental research on nonlinear geometric large deformation, temperature field large gradients, and quantitative identification of structural cracks. It is also used in practical engineering applications, such as the improvement design of paper-feeding mechanisms in office machinery, the gold-embossing die-cutting machine in the printing and packaging industry, and the crack fault diagnosis of railway track switch mechanisms. This book can serve as a reference or teaching material for undergraduate and graduate students in mechanical, energy, aerospace, and related fields, as well as for technical workers engaged in finite element dynamic analysis and design, dynamic design, and mechanical monitoring and diagnosis in relevant fields.