基于第二代小波的杆、梁单元构造研究

针对第二代小波尺度函数无显式表达式的缺点,提出采用PsdVoigt2函数进行拟合的方法,根据小波有限元及第二代小波理论,利用第二代小波尺度函数取代传统有限元多项式插值函数,通过转换矩阵将小波插值系数转换到物理空间,构造出形函数,并利用该方法构造一系列杆、梁单元。通过不同算例对构造的第二代小波杆、梁单元进行精度验证。计算结果表明,构造的第二代小波单元在求解变形和应变时精度较高,丰富了小波有限元单元库。

Study on construction of SGW-based bar-beam elements

PsdVoigt2 function was used to fit SGW function, and a series of bar beam elements based on the theory of SGW and wavelet finite element were constructed. Traditional finite element polynomial interpolation was replaced by the SGW scaling function, and transformation matrix was utilized to transform wavelet interpolation coefficients to physical space, then the shape function and a series of bar beam elements were constructed. The precision of constructed bar beam elements using SGW scale function as the interpolation function was verified by a series of calculation cases. The calculation results show that the SGW-based element has good precision in calculating the deformation and strain. The SGW-based bar beam element enriches the element library of wavelet-finite element method.