压电材料三维问题的虚边界元——最小二乘配点法

Virtual boundary element-least square collocation method for three dimensional piezoelectric materials

从压电材料三维问题的基本方程出发,利用已有的压电材料三维问题的基本解以及弹性力学虚边界元方法的基本思想和线性叠加原理,提出了压电材料三维问题的虚边界元——最小二乘配点解法。虚边界元解法继承了传统边界元方法的优点,并且有效避免了传统边界元方法中可能遇到的边界积分奇异性问题。最后,文章给出了压电材料三维问题的几个数值算例,并且与解析解做了比较,结果表明本文的方法具有较高的精度,是解决该问题一个十分有效的数值求解方法。

Based on the foundational solutions of three dimensional piezoelectric materials, the basis idea of virtual boundary element method for elasticity and the linear superposition principle, this paper present a virtual boundary element-least square collocation method for three dimensional piezoelectric materials. Except the same merits as the conventional boundary element method, the most important advantage of this method is it can exclude the singular integral in conventional boundary element method. In the end, numerical solutions are compared with analytical ones to demonstrate the validity and high accuracy of the method.