压电层合板的B样条小波有限元半解析法

Semi-analytical solution of B-spline wavelet-based finite element for piezoelectric lamina

  • 摘要: 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。

     

    Abstract: Some static problems of hybrid laminated plates with composite and piezoelectricity can be expediently solved by taking the advantage of wavelet finite element methods. Based on the features of laminated structures,the scale function of B-spline wavelet on the interval (BSWI) was employed to discretize the domain in-plane of structure,and the BSWI element formula of Hamilton canonical equation for piezoelectric materials was established by employing the modified mixed H-R( Hellinger-Reissner) variational principle for piezoelectric materials. One of the main characteristics of the BSWI element is the analytical form in the direction with respect to thickness. For the solution of the specific problem to ensure the interlaminar continuity of the electricity and mechanics variables,the transfer matrix technique was used. Numerical examples show that the BSWI element presented in the paper is successful. Employing the approach to deriving the BSWI element formula for piezoelectric materials can be extended to establish the analogous BSWI element formula for magnetoelectroelastic materials.

     

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