Wavelet Finite Element Method Of Hamilton Canonical Equation

Hamilton canonical equation theory of Elasticity when is employed to deal with the problems relative to the laminated plate, it holds a number of unique advantages. However, for sharp gradient problems or singularity of problems, there exit the same problems in semi-analytical method as the traditional finite element method. Only refine a mesh or improve the order of polynomial functions for high-precision results, but the computational load is heavy. The wavelet finite element method which takes the wavelet function as a basis set, holds the auto-adapted function, the algorithm with good stability, the operating speed quick and the result precision high; In processing local stress singularity problems, it has the attractive superiority. In order to take the full advantages of the wavelet finite element method and the Hamilton canonical equation, this thesis main subject is to combine both of them and to solve the related problems of composite materials laminated struction.Generally speaking, on the one hand, theoretically, this thesis given out the detail process from which derived the formulations of the Hamilton canonical equation of the B-spine wavelet and the second generation wavelet; On the other hand, employed the Mathematica language, programed the corresponding numerical analysis code, and confirmed the correct of two kind of wavelet finite element method through the use of the examples.Three parts are mainly included in this thesis:First, based on the semi-analytical solution of the Hamilton canonical equation and the traditational wavelet finite element method in the Lagrange systems, the formulations of the wavelet finite element for the Hamilton method were derived in detail.Next, three-dimensional model of the compound materials laminated plate with servral of boundary conditions were established, and the natural frequency solution formula and the internal stress formulatins of the laminated structure were deduced. Through comparing with the the results of ANSYS software's model, the Hamilton canonical equation's wavelet finite element method is confirmed effective, accurate.Finally, the formulation of the Hamilton canonical equation relative to the second generation wavelet function had been studied. As limited time, only the example relative to the displacement's solution were given and compared with the result of ANSYS software.