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利用小波有限元法的优越性可方便地求解压电材料与复合材料混合层合板的某些静力学问题。根据层合结构的特点,将区间B样条尺度函数作为插值函数离散结构的平面域,应用压电材料修正后的H-R(Hellinger-Reissner)变分原理推导了压电材料的Hamilton正则方程的区间B样条小波(BSWI)元列式。该BSWI元的主要特点之一是厚度方向是解析解形式的。针对具体问题的求解,为了保证各层之间力学量和电学量的连续性,进一步应用了状态转移矩阵技术。数值算例表明所提出的区间B样条小波单元是成功的。采用推导压电材料BSWI元的方法可建立磁电弹性材料类似的BSWI元。
By using the advantages of wavelet finite element method, some static problems of piezoelectric composite laminates can be easily solved. According to the characteristics of the laminated structure, the interval B-spline scaling function is used as the plane domain of the discrete structure of the interpolation function. The interval of the Hamilton’s canonical equation of the piezoelectric material is derived from the modified Hellinger-Reissner (HR) principle of the piezoelectric material B - spline wavelet (BSWI) metamodel. One of the main features of the BSWI element is that the thickness direction is analytically resolved. In order to solve the specific problems, in order to ensure the continuity of mechanics and electrical quantities between layers, the state transition matrix technique is further applied. Numerical examples show that the proposed interval B spline wavelet unit is successful. The BSWI element similar to the magnetoelastic material can be established by deriving the BSWI element of piezoelectric material.