薄板的多变量小波有限元分析

基于区间B样条小波和广义变分原理,提出了多变量小波有限元法,构造了一种新的薄板多变量小波有限单元.由广义变分原理推导结构的多变量有限元列式,区间B样条小波尺度函数作为插值函数构造的多变量小波有限元法中,广义应力和应变被作为独立变量进行插值,避免了传统方法中应力应变求解的微分运算,减小了计算误差.区间B样条小波良好的数值...

MULTIVARIABLE WAVELET FINITE ELEMENT METHOD FOR THIN PLATE ANALYSIS

Abstract: Based on B-spline wavelet on the interval and generalized potential variational principle, a new multivariable wavelet finite element method was proposed in this study, and the new corresponding elements for square and skew thin plate were constructed. Firstly, formulations were derived from multivariable generalized potential energy functional. Then the matrix equation of thin plate was obtained by using BSWI as trial function. In this study, the generalized stress and strain were interpolated separately, so differentiation of displacement in traditional method of stress calculation was avoided, and the calculation error was reduced. Besides, the good approximation property of B-spline wavelet on the interval can further guarantee the solving accuracy. In the end, several numerical examples for bending and vibration analysis of square and skew thin plate verified the efficiency and superiority in solving generalized stress.