用于各向异性压电材料的边界元法

给出一种用于压电材料静态问题的简单积分方程式.将压电体的控制方程按分离出各向同性及非耦合加权的形式进行重写,使各向同性弹性和势场问题的基本解可以通过积分方程列式表达,而另外两个补充方程通过压电材料的本构方程加以表达.最终,将耦合的各向异性问题转化为求解包含4个未知矢量的矩阵方程组.通过一个压电梁的计算实例说明了此方法的适用性.

A Boundary Element Method for Anisotropic Piezoelectric Media

A boundary element method(BEM) for solving homogeneous anisotropic piezoelectric problem is presented.The formulation procedure is developed by rewriting the piezoelectric governing equations and using the isotropic elastic and potential fundamental solutions,and the two unknown volume integrals are derived from the Somigliana's identity.The last formulation is four integral equations including four unknown vectors.Although the volume discretion is needed,the solution of the problem is only dependent on the boundary values by eliminating the unknown volume vectors through matrix analysis.A numerical example of piezoelectric bridge is presented to assess the accuracy of the proposed formulation and the method has been validated.