Daubechies条件小波Galerkin法在结构基本构件计算中的应用

APPLICATION OF DAUBECHIES CONDITIONAL WAVELET GALERKIN METHOD IN COMPUTATION OF STRUCTURAL FUNDAMENTAL COMPONENTS

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 promote the application of wavelet theory in structural computation,Daubechies wavelet Galerkin method is studied to computate the structural fundamental components.Because the displacement curve solved by the present Daubechies wavelet Galerkin method is not continuous,computation of high precision is hard to conduct.Combining with generalized variational principle and Lagrangian multiplier method,Daubechies wavelet Galerkin method could be modified to form Daubechies conditional wavelet Galerkin method to be employed in structural computation.Taking the structural fundamental components—bar and beam for examples,the construction of Daubechies conditional wavelet Galerkin method is elaborated.And the new method is compared with common FEM and present Daubechies wavelet Galerkin method at the same time.Typical computation examples were used to verify the accuracy of Daubechies conditional wavelet Galerkin method.