欧拉弯曲梁三次 Hermite 区间样条多小波有限元分析

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.

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

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.