CAJ | 학술논문

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。
침대제이대소파척도함수무현식표체식적결점，제출채용PsdVoigt2함수진행의합적방법，근거소파유한원급제이대소파이론，이용제이대소파척도함수취대전통유한원다항식삽치함수，통과전환구진장소파삽치계수전환도물리공간，구조출형함수，병이용해방법구조일계렬간、량단원。통과불동산례대구조적제이대소파간、량단원진행정도험증。계산결과표명，구조적제이대소파단원재구해변형화응변시정도교고，봉부료소파유한원단원고。
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.