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

Abstract

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.

On the topological enrichment for crack modeling via the generalized/extended FEM: a novel discussion considering smooth partitions of unity

“…where a translation and a scaling are performed for each function of this set [similar to (Torres and Mendonça, 2010;Torres et al, 2011)] to reduce mesh dependencies and round-off errors (Duarte et al, 2000). The first enrichment function of equation (10), for example, is given by the normalized coordinate x such as x :¼ x À x a ð Þ=ha x , with the x-coordinate x a of the node used for translation and the characteristic length h a x of the cloud, taken as the xprojection of the largest distance from the node x a to each of their cloud edges, used for scaling.…”

An efficient hybrid plate model for accurate analysis of smart composite laminates

“…Numerical implementation of this would require handling element-wise different values of geometry and material parameters and also variable number of DOF per element. Torres and Mendonca (2010) analyzed the coupled electrostructural response of laminated plates with orthotropic fiber-reinforced layers and piezoelectric layers using the generalized finite element method (GFEM). In this model, the mechanical displacements are modeled using HSDT, and electrical unknowns are modeled piece-wise linear along the thickness of the piezoelectric layers using layer-wise theory.…”