应用Daubechies小波理论求解应力大梯度梁

介绍了采用常规有限元法求解应力大梯度问题的缺点,指出小波理论具有多尺度、多分辨及紧支性等特性,应用小波理论计算应力大梯度问题将明显优于传统有限元法.以求解受集中荷载的平面弯曲梁为例,阐述了采用Daubechies小波理论进行计算时矩阵方程的建立及采用系数转换法施加本质边界条件的过程.分析系数转换法带来的不足,并结合广义变分原理对目前常用的Daubechies小波方法进行改进.通过实际算例中Daubechies小波方法的计算结果与理论解的对比验证应力大梯度问题计算中小波方法的有效性.

Applying Daubechies wavelet theory to compute beam of high stress gradient

The shortcoming of employing traditional finite element method to solve the problem of high stress gradient is introduced;and then the special characteristics of wavelet theory such as multi-scale,multi-resolution and compact support,are pointed out.So the wavelet theory has obvious superiority to solve the problem of high stress gradient than the traditional finite element method.Taking the plane bending beam bearing concentrated load for example,the construction of matrix equation and the procedure of using coefficient converting method to exert the essential boundary condition is described when applying Daubechies wavelet theory to calculate the beam.The disadvantage of coefficient converting method is analyzed.And we could improve the present Daubechies wavelet method by combining it with generalized variational principle.At last,through the comparison between the computation results of Daubechies wavelet method and the theoretical values,the validity of Daubechies wavelet method for solving the problem of high stress gradient is verified.