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Exact solutions for simply supported functionally graded piezoelectric laminates by Stroh-like formalism

机译：类似于Stroh形式主义的简单支撑功能梯度压电层压板的精确解决方案

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摘要

This paper presents an alternative method for the derivation of exact solutions of a simply supported rectangular functionally graded piezoelectric plate or laminate. In the approach, the related equations and formulas are developed in terms of an elegant formalism similar to the Stroh formalism, which can be expressed in more concise and easier handling forms comparing to the approach used in literature for the problems [Zhong Z, Shang ET. Three-dimensional exact analysis of a simply supported functionally gradient piezoelectric plate. Int J Solids Struct 2003;40:5335-52]. Numerical examples for a single plate with functionally graded piezoelectric material (FGPM) and a two-layer FGPM laminated plate are presented. Based on the results, the validity range of 2-D thin plate theories, and the influences of material gradient index and layer thickness on interfacial and surface properties of a FGPM laminate under mechanical and/or electrical forces are discussed.
机译：本文提出了另一种方法，用于推导简单支撑的矩形功能梯度压电板或层压板的精确解。在该方法中，相关方程和公式是根据类似于Stroh形式主义的优雅形式主义开发的，与文献中针对问题的方法相比，它可以更简洁，更易于处理的形式表示[Zhong Z，Shang ET 。简单支撑的功能梯度压电板的三维精确分析。 Int J Solids Struct 2003; 40：5335-52]。给出了具有功能梯度压电材料（FGPM）的单板和两层FGPM层压板的数值示例。基于这些结果，讨论了二维薄板理论的有效性范围，以及材料梯度指数和层厚度对机械力和/或电力下FGPM层压板的界面和表面性能的影响。

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