APPLICATION OF DAUBECHIES CONDITIONAL WAVELET MIXED FINITE ELEMENT METHOD IN NUMERICAL COMPUTATION OF BEAMS

The conventional Daubechies wavelet Finite Element Method is a kind of single variable Finite Element Method using a deflection function as a basic unknown function. Its bending moment function has to be calculated indirectly by calculating the second derivative of the deflection function. Thusly the accuracy of bending moments is always worse than deflection. Furthurmore, in the present Daubechies wavelet Finite Element Method, the leading of displacement boundary conditions has to draw a support from a converting matrix and then obviously influences the computation accuracy. Employing the Generalized Variational Principle, and taking a boundary condition as a subsidiary condition, a modified functional can be constructed. Consequently the solving matrix equation can be constructed utilizing the arrest point condition of the modified functional to obtain the unknown field function. This method can effectively promote the calculation accuracy, and it is called Daubechies conditional wavelet Finite Element Method. Based on the method and leading Hellinger-Reissner Generalized Variational Principle, using force and displacement functions as interpolating functions, the Daubechies conditional wavelet mixed Finite Element Method can be constructed. In this method, we can solve the force and displacement functions together, and the solution of the internal force is independent with the displacement. So the accuracy of internal force calculation is higher. The solution of an equation in Daubechies conditional wavelet mixed Finite Element Method is inferred by the technique based on beam elements. And through examples the practical applicability and validity of the new method are testified.