【摘要】 为了有效地实现有限元自适应分析中函数平滑逼近和细节信息的分离,根据提出的第二代小波有限元多分辨分析方法构造了相应的自适应算法.采用第二代小波作为基函数构造了逐级嵌套的有限元逼近空间,并引入消失矩提出有限元求解方程刚度矩阵解耦的条件.函数在低分辨空间的逼近可以通过增加细节空间提升到高分辨空间,通过使刚度矩阵解耦,可以消除低分辨逼近空间和细节空间之间以及不同尺度的细节空间之间的耦合项.通过构造轴力杆的自适应分析,验证了方法的有效性,同时为实现复杂第二代小波自适应有限元分析提供了较好的研究思路.更多还原

【Abstract】 Based on second generation wavelets(SGW), a multiresolution finite element method is presented,and the corresponding adaptive algorithm is constructed.The hierarchical approximation spaces for finite element analysis are produced and the decoupling condition of the stiffness matrix of the finite element equation is established by introducing wavelet vanishing moments.The finite element equation is scale-decoupled via eliminating all coupling in the stiffness matrix of the finite element equation across scales, then resolved in different spaces independently.The coarse solution can be obtained in the coarse approximation space,and refined by adding details in the detail spaces over several levels till the equation is resolved with the desired accuracy.The numerical example of axial bar verifies the effectiveness of this method.更多还原