Theory Of Wavelet Finite Element Method And Its Applications In Structure Engineering

Wavelet theory is a mathematic tool that is took shape and developed in recent. It has raised more attentions in engineer fields, specially in signal analysis, images handles, pattern recognition, phonetic recognition, quantum physics, earthquake reconnaissance, fluid mechanics, electromagnetic field, CT imagery, diagnosis and monitoring of machinery defect, fractal, numerical evaluation et al. It is considered as important breakthrough in methods and tools. Wavelet analysis based on wavelet transform is the most perfect combination of functional analysis, Fourier transform, spline analysis, harmonic analysis and numerical analysis at present, it is a new developing branch in mathematic. Although some scholars solved differential equations of structure engineering using wavelet, there have some defects. Such as the scaling function and wavelet function have not definit expression, some troubles existed in calculating connection coefficients, its values is instability in some times and so on. The object of this thesis is to find some new methods solving differential equation. Thesis combines usually finite element method (FEM) and wavelet analysis, wavelet FEM is put forth creativitily for structure engineering. At the same time, in order to analysis some indeterminacy of structure for example physics and geometric parameter, constraint conditions, stochastic wavelet FEM is proponed. Those methods make the applications of wavelet in structure engineering become more extensive.At first, this thesis gives right calculation results of derivative of Daubechies scaling function, the determine fashion of continuity is rendered. In solving differential equations, we must increase supported assemble length since the continuity of Daubechies wavelet derivative increases as supported assemble increase, that results in calculation complexly. In guarding the continuity of derivative and not increasingsupported assemble, this paper uses convolution of Daubechies and B-spline scale functions to improve original method. M-scale function is constructed, two-scale function, which often is used to solve differential equations, is its special conditions. Three-scaling spline wavelets and wavelet Galerkin method are used to solve some problems.Adding boundary conditions in whole equations in the wavelet Galerkin method frequently does with its of differential equations. The result can derive by solving transcendental equation, which make unknow quantity number and the number of system of equation become nonuniformity. For those, this thesis constructions the Hermite B-spline bases scale functions with boundary conditions on the interval. Combining with Garlerkin method, the steps are given to solve differential equation, as an example, it is used to deal with finite-length beam and plate problems. This thesis gives the B-spline wavelet and essential quality of it, proponing the solving array expression of combining B-spline wavelet and Galerkin method.This thesis first presents a multivariable wavelet FEM that is based on Hellingger-Reissner and Hu-Washizu variational principle. The interpolating wavelet bases are constructed in order to deal with boundary conditions conveniently at first. Then the wavelet bases of duality in product form are used to construct the generalized field functions of beam, plate and shell. The model of multivariable wavelet FEM is built by Hellingger-Reissner and Hu-Washizu generalized variational principle. In calculating variables, the stress-strain relations and the differential calculation are not implemented, so all kinds of variable have enough precision. But this universe wavelet FEM displays its superiority only in regulation figure fields. Through the processing of solving beam, plate and shell in structure must transit generalized variational principle respective, so the commonality is difference.The displacement functions in usually FEM are constructed with wavelet functions, then the form functions expression with wavelet functions. For the first time wavelet FEM of dividing...