欧拉弯曲梁三次Hermite区间样条多小波有限元分析  

Finite element analysis of Euler beam using multi-wavelets based on cubic Hermite spline function on interval

作　　者：夏逸鸣[1,2] 唐敢[2,3] 江世永[1] 

机构地区：[1]解放军后勤工程学院土木工程系,重庆400042 [2]南京航空航天大学土木工程系,江苏南京210016 [3]东南大学土木工程学院,江苏南京210096

出　　处：《河海大学学报（自然科学版）》2012年第3期313-318,共6页Journal of Hohai University(Natural Sciences)

基　　金：国家自然科学基金(51008067);航空科学基金(2010ZA52009);南京航空航天大学基本科研业务费项目(NS2010018;2010ZA52009);江苏省六大人才高峰项目;住房和城乡建设部科学技术计划项目(2011-K1-68)

摘　　要：基于小波多辨分析思想,选择三次Hermite区间样条函数作为多小波尺度基函数,用于构建梁单元多尺度位移近似空间;由最小势能原理,推导出欧拉弯曲梁有限元平衡方程.结果表明:该小波单元可通过改变多小波尺度函数的尺度来重新划分网格,从而可自由调节小波单元的计算精度;其计算精度与采用具有相同网格划分的任意多个传统欧拉弯曲梁单元求解的精度完全相同;该小波单元更加清晰地反映了小波有限元与传统有限元之间的关联.Based on the wavelet multi-resolution concept, this paper presents the formulation of the Euler beam element using multi-wavelets based on the cubic Hermite spline function on the interval. According to the principle of minimum potential energy, the finite element equilibrium equation for the Euler beam was deduced. The results show that the calculation accuracy of the wavelet element could be voluntarily adjusted by changing the scaling level and grid repartitioning, and it was the same as that of traditional Euler beam elements with equivalent grids. In addition, this wavelet element presented the correlation between the wavelet finite element and traditional finite element in a more explicit manner than other wavelet elements.

关 键 词：三次Hermite区间样条函数 尺度函数 多小波 有限元 

分 类 号：TU375.1[建筑科学—结构工程]