用裂纹单元分析双压电材料界面力电耦合奇异场

ANALYSIS OF SINGULAR ELECTROMECHANICAL FIELDS AT THE INTERFACES OF BIMORPH WITH A “CRACKED ELEMENT”

为了求解双压电材料在机械荷载和(或)外加电场的作用下,界面裂纹尖端的力电耦合奇异场,提出了一种全数值方法。该全数值方法的实施可以分为两个部分:首先,用一维有限元方法求解不同压电材料界面裂纹尖端力电耦合奇异场特征解;然后,采用杂交有限元列式构造一种所谓的裂纹单元,在该杂交有限元的列式中,假设应力场和电位移场是利用上述一维有限元方法计算得到的特征解推导出来的;利用该单元可以得到全部的力电耦合奇异场的解。通过对单一压电材料中心裂纹尖端力电耦合奇异场的计算,该方法的准确性和高效性得到了验证;进而用该方法研究了双压电材料界面力电耦合场奇异场。

A full numerical procedure is proposed in order to compute the singular electromechanical field at the interfaces of bimorph. The whole procedure consists of two steps： （1） an ad hoc one-dimensional fmite element formulation, which is developed by Wang ＆ Sze, is employed to determine the eigensolution of the singular electromechanical field; （2） a hybrid crack element is constructed to determine the strength of the singular electromechanical field. The independent assumed stress and electrical displacement fields are extracted from the eigensolution obtained from previous ad hoc one-dimensional finite element formulation. The reliability and efficacy of the proposed procedure are verified through a numerical example of a central crack in a homogeneous piezoelectric panel. The proposed procedure is used to study the singular electromechanical fields at the interfaces ofbimorph.