摘要
利用样条小波尺度函数构造了常用的三角形和矩形薄板单元的位移函数,得到了利用小波函数表示的形函数。采用合理的局部坐标,对单元进行压缩,使单元在局部坐标区间上有其值,成功地推导出了分域的三角形和矩形薄板小波有限元列式。在此基础上,提出了弹性地基薄板的小波有限元求解方法。通过两个算例对薄板的挠度和弯矩进行了计算,数值结果表明,求解结果具有收敛快、精度高的特点。
Wavelet scaling functions of spline wavelets are used firstly to construct displacement functions of triangular and rectangular thin plate elements in finite element method. So displacement shape functions can be expressed by wavelet functions. Selecting convenient local coordinates and compressing elements, which make elements having their values in interval in local coordinates. Wavelet finite element expressions of triangular and rectangular elements in dividing domain of thin plate are derived through the principle of virtual work. The wavelet finite element method used to selve thin plate of elastic foundation is presented. This work represents the first attempt in using wavelet functions in finite element method of dividing domain. Numerical analysis of two examples demonstrates the deflection and moment of thin plate are consistent with those obtained with analytical solution, which illustrates that the wavelet finite element method has better convergence and higher accuracy.
出处
《计算力学学报》
EI
CAS
CSCD
北大核心
2006年第1期76-80,123,共6页
Chinese Journal of Computational Mechanics
基金
国家自然科学基金(59978038)资助项目
关键词
小波函数
小波有限元
薄板
弹性地基
wavelet functions
wavelet finite element
thin plate
elastic foundation
