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为拓展小波理论在结构计算中的应用,研究采用Daubechies小波Galerkin法计算结构基本构件。现有的Daubechies小波Galerkin法所解出的位移曲线不连续,无法实现高精度计算。结合广义变分原理及Lagrange乘子法,对Daubechies小波Galerkin法进行改进,形成Daubechies条件小波Galerkin法并应用于结构计算。以结构中最为常见的基本构件——杆、梁为例,阐述Daubechies条件小波Galerkin法的构成方法,并与常规有限元法及现有Daubechies小波Galerkin法进行比较。通过典型算例,验证Daubechies条件小波Galerkin法的计算精度。
In order to expand the application of wavelet theory in structural calculation, Daubechies wavelet Galerkin method is used to calculate the basic structure of the structure. The displacement curve obtained by the existing Daubechies wavelet Galerkin method is not continuous and can not be calculated accurately. Combined with generalized variational principle and Lagrange multiplier method, the Daubechies wavelet Galerkin method is improved to form Daubechies conditional wavelet Galerkin method and applied to structural calculation. Taking the beam and beam, the most common basic structure in the structure, as an example, the composition method of Daubechies conditional wavelet Galerkin method is illustrated and compared with the conventional finite element method and the existing Daubechies wavelet Galerkin method. Through a typical example, the computational accuracy of the Daubechies conditional wavelet Galerkin method is verified.