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Analysis of piezoelectric laminates by generalized finite element method and mixed layerwise-HSDT models

机译:压电层合板的广义有限元分析和混合分层HSDT模型

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This paper presents a procedure to numerically analyze the coupled electro-structural response of laminated plates with orthotropic fiber reinforced layers and piezoelectric layers using the generalized finite element method (GFEM). The mechanical unknowns, the displacements, are modeled by a higher order shear deformation theory (HSDT) of the third order, involving seven generalized displacement functions. The electrical unknowns, the potentials, are modeled by a layerwise theory, utilizing piecewise linear functions along the thickness of the piezoelectric layers. All fields are enriched in the in-plane domain of the laminate, according to the GFEM, utilizing polynomial enrichment functions, defined in global coordinates, applied on a bilinear partition of unities defined on each element. The formulation is developed from an extended principle of Hamilton and results in a standard discrete algebraic linear motion equation. Numerical results are obtained for some static cases and are compared with several numerical and experimental results published in the literature. These comparisons show consistent and reliable responses from the formulation. In addition, the results show that GFEM meshes require the least number of elements and nodes possible for the distribution of piezoelectric patches and the enrichment provides more flexibility to reproduce the deformed shapes of adaptive laminated plates.
机译:本文提出了一种程序,使用广义有限元方法(GFEM)来数值分析具有正交各向异性纤维增强层和压电层的层合板的电结构响应。机械未知数(位移)是通过三阶的高阶剪切变形理论(HSDT)建模的,其中涉及七个广义位移函数。电未知数,电势通过分层理论建模,利用沿着压电层厚度的分段线性函数。根据GFEM,利用在全局坐标中定义的多项式富集函数,将所有字段在层状结构的平面内域中富集,这些函数应用于在每个元素上定义的单位的双线性分区上。该公式是根据汉密尔顿的扩展原理开发的,并得出标准的离散代数线性运动方程。获得了一些静态情况下的数值结果,并将其与文献中发表的一些数值和实验结果进行了比较。这些比较显示了该制剂的一致和可靠的响应。此外,结果表明,GFEM网格需要尽可能少的元素和节点来分布压电贴片,并且富集为再现自适应层压板的变形形状提供了更大的灵活性。

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