摘要
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逼近性能可进一步保证求解精度.通过方形薄板、斜形薄板以及梯形薄板的弯曲和振动分析,验证了此方法的有效性和在广义应力求解中的优越性.
Based on B-spline wavelet on the interval（BSWI） and the generalized potential variational principle,a new multivariable wavelet finite element method with two kinds of variables was proposed in the paper.The new corresponding elements for square thin plate,skew thin plate and trapezoidal 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.Finally,several numerical examples for bending and vibration analysis of square and skew thin plate verified the efficiency and superiority in solving generalized stress.
出处
《固体力学学报》
CAS
CSCD
北大核心
2011年第2期210-216,共7页
Chinese Journal of Solid Mechanics
基金
国家自然科学基金项目(50875195)
全国优博专项基金项目(2007B33)资助
关键词
多变量
区间B样条小波
薄板
弯曲
振动
multivariable
B-spline wavelet on the interval
thin plate
bending
vibration
