The aim of the present study is to present an effect boundary element method (BEM) for electroelastic analysis of ultrathin piezoelectric films/coatings. The troublesome nearly singular integrals, which are crucial in applying the BEM for thin‐structural problems, are calculated accurately by using a nonlinear coordinate transformation method. The advanced BEM presented requires no remeshing procedure regardless of the thickness of the thin structure. Promising BEM results with only a small number of boundary elements can be achieved with the relative thickness of the thin piezoelectric film is as small as 10⁻⁸, which is sufficient for modeling many ultrathin piezoelectric films as used in smart materials and micro‐electro‐mechanical systems. The present BEM procedure with thin‐body capabilities is also extended to general multidomain problems and used to model ultrathin coating/substrate piezoelectric structures. The influence of relative layer‐to‐substrate thickness and the bimaterial mismatch parameters are carefully investigated. Excellent agreement between numerical and theoretical solutions has been demonstrated.

中文翻译：

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二维超薄压电薄膜的先进边界元法电弹性分析

本研究的目的是提出一种效应边界元方法（BEM），用于超薄压电薄膜/涂层的电弹性分析。使用非线性坐标变换方法可以准确地计算出麻烦的近奇异积分，这些积分对于将BEM应用到薄结构问题中至关重要。不论薄型结构的厚度如何，提出的高级BEM都不需要重新镶嵌程序。薄压电膜的相对厚度小至10 ^-8时，仅需少量边界元素即可获得令人满意的BEM结果，这足以对智能材料和微机电系统中使用的许多超薄压电薄膜进行建模。当前具有薄体功能的BEM程序也扩展到一般的多域问题，并用于建模超薄涂层/基底压电结构。仔细研究了相对的层对基底厚度和双材料失配参数的影响。已经证明了数值解和理论解之间的极好的一致性。