Finite element modeling for buckling analysis of hybrid piezoelectric beam under electromechanical loads

Abstract

A one-dimensional finite element model for buckling analysis of hybrid piezoelectric beams under electromechanical load is presented in this work. The coupled zigzag theory is used for making the model. The inplane displacement is approximated as a combination of a global third order variation across the thickness with an additional layer wise linear variation. The longitudinal electric field is also taken into account. The deflection field is approximated to account for the transverse normal strain induced by electric fields. Two nodded elements with four mechanical and a variable number of electric degrees of freedom at each node are considered. To meet the convergence requirements for weak integral formulation, cubic Hermite interpolation function is used for deflection and electric potential at the sub-layers and linear interpolation function is used for axial displacement and shear rotation. The expressions for the variationally consistent stiffness matrix and load vector are derived and evaluated in closed form using exact integration. The present 1D-FE formulation of zigzag theory is validated by comparing the results with the analytical solution for simply-supported beam and 2D-FE results obtained using ABAQUS. The finite element model is free of shear locking. The critical buckling parameters are obtained for clamped-free and clamped-clamped hybrid beams. The obtained results are compared with the 2D-FE results to establish the accuracy of the zigzag theory for above boundary conditions. The effect of lamination angle on critical buckling load is also studied.

Quasicomparison Functions and Substructure Synthesis for Framed Structures Stability Analysis

“…Areny et al (2011) have also worked on linear structural stability using substructuring; nevertheless, the concentration was on a new uncertainty propagation method based on the concept of lack of knowledge, which comes from the field of Model Updating; interestingly, there is an application of the RRMSSM in Model Updating (Halevi et al, 2005). Rahman and Alam (2014) have dealt with buckling in hybrid piezoelectric beams under electromechanical load; on the other hand, da Mota et al (2015) have worked on nonlinear stability of piles subjected to bilateral contact constraints underground. In these two cases, the FEM is by far the preferred method; in the first case the coupled zig zag theory is the basis for the FEM.…”

Finite element modelling to assess the effect of position and size of the piezoelectric layer of a hybrid beam

“…The Najeeb ur Rahman a * M. Naushad Alam a consideration of electric nodes result in significant reduction in the number of electric degrees of freedom. Rahman and Alam 2012, 2014 used layerwise zigzag theory for 1D-FE modelling of smart laminated beam. Kapuria and Kulkarni 2008 proposed an efficient four-node quadrilateral element using zigzag theory for the dynamic analysis of hybrid plates with segmented piezoelectric sensors and actuators.…”

Shear wave propagation in piezoelectric-piezoelectric composite layered structure

“…The effect of imperfect bonding on interfacial waves in dissimilar piezoelectric composite has been studied by Huang, and Li extensively (2011). Recently some researchers have revealed the imperfect bonding is major cause in dispersion of shear wave propagation in PE-PM interface (Melkumyan et al 2008, Huang et al 2009, and Rahman et al 2014. In past decade, research work focused much on shear wave propagation in piezoelectric-piezomagnetic interface, but no work was reported so far on shear wave propagation in piezoelectric-piezoelectric composites.…”