Static Analysis of a Functionally Graded Piezoelectric Beam Using Finite Element Method

2010 ◽  
Author(s):  
Iman Eshraghi ◽  
Aghil Yousefi-Koma
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shear Deformation ◽  
Static Analysis ◽  
Slenderness Ratio ◽  
Beam Theory ◽  
Functionally Graded ◽  
Bending Behavior ◽  
Functionally Graded Piezoelectric ◽  
Element Method

In this study static analysis of functionally graded piezoelectric material (FGPM) beams is performed using finite element modeling. First order shear deformation beam theory (Timoshenko beam theory) with the assumption of linear strain-displacement relations is used for modeling of displacement and strain fields in the beam. Theoretical formulations are derived employing Hamilton’s principle using linear constitutive relations of piezoelectric materials and including the effect of transverse shear deformation. Finite element method with one dimensional linear continuum isoparametric element, three displacement mechanical degrees of freedom, and one electric potential degree of freedom assigned to each node is then used to investigate the bending behavior of FGPM beam actuator under thermo-electro-mechanical loads. Consequently, a parametric study of the bending behavior of an FGPM beam is performed. The effects of slenderness ratio and fraction of volume of constituent materials, on the thermo-electro-mechanical characteristics are studied. It is shown that under electrical loading the beam represents the so-called non-intermediate behavior.

Analysis of bimorph piezoelectric beam energy harvesters using Timoshenko and Euler–Bernoulli beam theory

2012 ◽  
Vol 24 (2) ◽  
pp. 226-239 ◽  
Author(s):  
Gang Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Slenderness Ratio ◽  
Beam Theory ◽  
Bernoulli Beam ◽  
Energy Harvesters ◽  
Bernoulli Beam Theory ◽  
Spectral Finite Element ◽  
Euler Bernoulli Beam ◽  
Element Method

Single-degree-of-freedom lumped parameter model, conventional finite element method, and distributed parameter model have been developed to design, analyze, and predict the performance of piezoelectric energy harvesters with reasonable accuracy. In this article, a spectral finite element method for bimorph piezoelectric beam energy harvesters is developed based on the Timoshenko beam theory and the Euler–Bernoulli beam theory. Linear piezoelectric constitutive and linear elastic stress/strain models are assumed. Both beam theories are considered in order to examine the validation and applicability of each beam theory for a range of harvester sizes. Using spectral finite element method, a minimum number of elements is required because accurate shape functions are derived using the coupled electromechanical governing equations. Numerical simulations are conducted and validated using existing experimental data from the literature. In addition, parametric studies are carried out to predict the performance of a range of harvester sizes using each beam theory. It is concluded that the Euler–Bernoulli beam theory is sufficient enough to predict the performance of slender piezoelectric beams (slenderness ratio > 20, that is, length over thickness ratio > 20). In contrast, the Timoshenko beam theory, including the effects of shear deformation and rotary inertia, must be used for short piezoelectric beams (slenderness ratio < 5).

Analysis of bi-directional functionally graded sandwich plates via higher-order shear deformation theory and finite element method

2021 ◽  
pp. 109963622110258
Author(s):  
Pham Van Vinh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Sandwich Plates ◽  
Element Method

This paper introduces a comprehensive investigation of bi-directional functionally graded sandwich plates using higher-order shear deformation theory and finite element method for the first time. A special procedure incorporating with a bi-linear four-node quadrilateral element is used to treat the free condition of shear stresses on two surfaces of the sandwich plates. Four types of the bi-directional functionally graded sandwich plates with several thickness ratios of layers are considered, in which the material properties of the layers are assumed to vary in both the thickness and the in-plane directions. The present results are compared with published data in some special cases to demonstrate the convergence and accuracy of the present algorithm. The investigations show that the variation of the material ingredients and properties, the boundary conditions, the thickness ratio of layers play significant roles on the bending, free vibration and buckling behaviors of bi-directional functionally graded sandwich plates.

Steady-State Responses of Functionally Graded Piezoelectric Structures by the Coupled Thermal-Electrical-Mechanical Inhomogeneous Cell-Based Smoothed Finite Element Method (CICS-FEM)

2020 ◽  
pp. 2050042
Author(s):  
Han Chen ◽  
Liheng Wang ◽  
Dongqi Li ◽  
Liming Zhou ◽  
Peng Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Steady State ◽  
Functionally Graded ◽  
Smart Devices ◽  
Smoothed Finite Element Method ◽  
Steady State Responses ◽  
Functionally Graded Piezoelectric ◽  
State Responses ◽  
Element Method

To accurately simulate the steady-state responses of a functionally graded piezoelectric structure (FGPS) and cure the “overly-stiff” of finite element method (FEM), the coupled thermal-electrical-mechanical inhomogeneous cell-based smoothed finite element method (CICS-FEM) is proposed. The gradient smoothing technique is introduced into FEM and a “close-to-exact” stiffness is obtained. Based on the basic theory of FGPS, the thermal field is introduced into the electrical-mechanical coupling field and the multi-physics coupling equations are given in conjunction with the cell-based smoothed finite element method. CICS-FEM is verified with several examples, and there is a satisfactory agreement between the current solution and the reference solution. Therefore, the developed method to solve the steady-state response of FGPS can provide a reference for the design and manufacture of smart devices.

scholarly journals A Coupling Electromechanical Inhomogeneous Cell-Based Smoothed Finite Element Method for Dynamic Analysis of Functionally Graded Piezoelectric Beams

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Bin Cai ◽  
Liming Zhou
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Piezoelectric Materials ◽  
Continuous System ◽  
Functionally Graded ◽  
Gaussian Integration ◽  
Functionally Graded Piezoelectric Materials ◽  
Smoothed Finite Element Method ◽  
Functionally Graded Piezoelectric ◽  
Element Method

To accurately simulate the continuous property change of functionally graded piezoelectric materials (FGPMs) and overcome the overstiffness of the finite element method (FEM), we present an electromechanical inhomogeneous cell-based smoothed FEM (ISFEM) of FGPMs. Firstly, ISFEM formulations were derived to calculate the transient response of FGPMs, and then, a modified Wilson-θ method was deduced to solve the integration of the FGPM system. The true parameters at the Gaussian integration point in FGPMs were adopted directly to replace the homogenization parameters in an element. ISFEM provides a close-to-exact stiffness of the continuous system, which could automatically and more easily generate for complicated domains and thus significantly decrease numerical errors. The accuracy and trustworthiness of ISFEM were verified as higher than the standard FEM by several numerical examples.

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