中文摘要：

常规的Daubechies小波有限元法是以挠度为基本未知量的单变量有限元法，其弯矩函数需要通过挠度函数的二阶求导间接求解，故弯矩的计算精度一般比挠度低。此外，目前常用的Daubechies小波有限元法需要借助于转换矩阵引入位移边界条件，大大影响了计算精度。结合广义变分原理，将边界条件作为附加条件构造修正泛函，以该修正泛函的驻值条件建立求解矩阵方程，进而解得未知场函数，可以有效提高计算精度，即为Daubechies条件小波有限元法。在此基础上，结合Hellinger-Reissner广义变分原理，以力和位移为插值函数，可以建立Daubechies条件小波混合有限元法。由于该法能一次同时解得位移与力的场函数，并且内力的求解独立于位移，因而内力的求解精度较高。以梁单元为例，推导出了Daubechies条件小波混合有限元方程，并通过算例验证了该方法的实用性和有效性。

英文摘要：

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 Daubeehies conditional wavelet Finite Element Method. Based on the method and leading HeUinger-Reissner Generalized Variational Principle, using force and displacement functions as interpolating functions, the Daubeehies 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.