摘要
研究了一类新的有限元空间,它以小波尺度函数作为插值函数,从而构造出了小波有限元.利用小波的两尺度方程,很好地解决了因Daubechies小波尺度函数无明确解析表达式造成的积分困难,推导出了小波有限元常用刚度矩阵及载荷列阵积分公式,并给出了小波有限元用于薄板弯曲的分析列式.通过薄板弯曲及办公纸张温度场的数值分析,表明小波有限元具有满意的分析精度,可消除由于温度梯度变化而引起的0 5%左右的数值失真,并在处理变边界条件等大梯度问题方面,优于传统的小波有限元.
A new finite element space is studied, in which the scaling functions of Daubechies wavelets are considered as the interpolation basis functions, and then the wavelet finite element (WFE) is constructed. In order to overcome the integral difficulty for lack of explicit scaling function expression, a new and efficient integral method for stiffness matrix and load matrix is presented by employing two-scale equations. The bending for a thin plate equations based on WFE is derived, and the bending characters of thin plate and the inner temperature distribution of office paper are studied. Numerical results indicate that WFE has desirable calculation precision and can eliminate 0.5% numerical distortion caused by temperature changes. WFE is superior to traditional finite element method while dealing with large gradient problem, such as suddenly changing boundary condition.
出处
《西安交通大学学报》
EI
CAS
CSCD
北大核心
2003年第1期1-4,共4页
Journal of Xi'an Jiaotong University
基金
国家自然科学基金资助项目(50175087)
西安交通大学博士学位论文基金资助项目(DFXJU1999-6).
