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.

scholarly journals An Inhomogeneous Cell-Based Smoothed Finite Element Method for Free Vibration Calculation of Functionally Graded Magnetoelectroelastic Structures

2018 ◽  
Vol 2018 ◽  
pp. 1-17 ◽  
Author(s):  
Yan Cai ◽  
Guangwei Meng ◽  
Liming Zhou
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Continuous System ◽  
Functionally Graded ◽  
Gaussian Integration ◽  
Stiffness Matrices ◽  
Inherent Frequency ◽  
Smoothed Finite Element Method ◽  
Element Method

To overcome the overstiffness and imprecise magnetoelectroelastic coupling effects of finite element method (FEM), we present an inhomogeneous cell-based smoothed FEM (ICS-FEM) of functionally graded magnetoelectroelastic (FGMEE) structures. Then the ICS-FEM formulations for free vibration calculation of FGMEE structures were deduced. In FGMEE structures, the true parameters at the Gaussian integration point were adopted directly to replace the homogenization in an element. The ICS-FEM provides a continuous system with a close-to-exact stiffness, which could be automatically and more easily generated for complicated domains, thus significantly decreasing the numerical error. To verify the accuracy and trustworthiness of ICS-FEM, we investigated several numerical examples and found that ICS-FEM simulated more accurately than the standard FEM. Also the effects of various equivalent stiffness matrices and the gradient function on the inherent frequency of FGMEE beams were studied.

An inhomogeneous cell-based smoothed finite element method for the nonlinear transient response of functionally graded magneto-electro-elastic structures with damping factors

2018 ◽  
Vol 30 (3) ◽  
pp. 416-437 ◽  
Author(s):  
Liming Zhou ◽  
Ming Li ◽  
Bingkun Chen ◽  
Feng Li ◽  
Xiaolin Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Element Model ◽  
Micro Electro Mechanical System ◽  
Functionally Graded ◽  
Elastic Structures ◽  
Mapping Procedure ◽  
Gaussian Integration ◽  
Smoothed Finite Element Method ◽  
Element Method

In this article, an inhomogeneous cell-based smoothed finite element method (ICS-FEM) was proposed to overcome the over-stiffness of finite element method in calculating transient responses of functionally graded magneto-electro-elastic structures. The ICS-FEM equations were derived by introducing gradient smoothing technique into the standard finite element model; a close-to-exact system stiffness was also obtained. In addition, ICS-FEM could be carried out with user-defined sub-routines in the business software now available conveniently. In ICS-FEM, the parameters at Gaussian integration point were adopted directly in the creation of shape functions; the computation process is simplified, for the mapping procedure in standard finite element method is not required; this also gives permission to utilize poor quality elements and few mesh distortions during large deformation. Combining with the improved Newmark scheme, several numerical examples were used to prove the accuracy, convergence, and efficiency of ICS-FEM. Results showed that ICS-FEM could provide solutions with higher accuracy and reliability than finite element method in analyzing models with Rayleigh damping. Such method is also applied to complex structures such as typical micro-electro-mechanical system–based functionally graded magneto-electro-elastic energy harvester. Hence, ICS-FEM can be a powerful tool for transient problems of functionally graded magneto-electro-elastic models with damping which is of great value in designing intelligence structures.

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 Dynamic Analysis of Functionally Graded Porous Plates Resting on Elastic Foundation Taking into Mass subjected to Moving Loads Using an Edge-Based Smoothed Finite Element Method

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Trung Thanh Tran ◽  
Quoc-Hoa Pham ◽  
Trung Nguyen-Thoi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Analysis ◽  
Elastic Foundation ◽  
Functionally Graded ◽  
Triangular Element ◽  
Moving Loads ◽  
Smoothed Finite Element Method ◽  
Edge Based ◽  
Element Method

The paper presents the extension of an edge-based smoothed finite element method using three-node triangular elements for dynamic analysis of the functionally graded porous (FGP) plates subjected to moving loads resting on the elastic foundation taking into mass (EFTIM). In this study, the edge-based smoothed technique is integrated with the mixed interpolation of the tensorial component technique for the three-node triangular element (MITC3) to give so-called ES-MITC3, which helps improve significantly the accuracy for the standard MITC3 element. The EFTIM model is formed by adding a mass parameter of foundation into the Winkler–Pasternak foundation model. Two parameters of the FGP materials, the power-law index (k) and the maximum porosity distributions (Ω), take forms of cosine functions. Some numerical results of the proposed method are compared with those of published works to verify the accuracy and reliability. Furthermore, the effects of geometric parameters and materials on forced vibration of the FGP plates resting on the EFTIM are also studied in detail.

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.

Coupled Thermal–Electrical–Mechanical Inhomogeneous Cell-Based Smoothed Finite Element Method for Transient Responses of Functionally Graded Piezoelectric Structures to Dynamic Loadings

2019 ◽  
Vol 17 (06) ◽  
pp. 1950012
Author(s):  
Guangwei Meng ◽  
Liheng Wang ◽  
Qixun Zhang ◽  
Shuhui Ren ◽  
Xiaolin Li ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Electrical Potential ◽  
Functionally Graded ◽  
Fe Model ◽  
Mesh Distortion ◽  
Contour Plots ◽  
Smoothed Finite Element Method ◽  
Gradient Smoothing ◽  
Element Method

A coupled thermal–electrical–mechanical inhomogeneous cell-based smoothed finite element method (CICS-FEM) is presented for the multi-physics coupling problems, the displacements, the electrical potential and the temperature are obtained by combining the modified Wilson-[Formula: see text] method. By introducing the gradient smoothing technique into the FE model, the system stiffness of the model is reduced. In addition, due to the absence of mapping, CICS-FEM is insensitive to mesh distortion. Curves and contour plots of displacements, electrical potential and temperature of three FGP structures are given in the article. The results shows that CICS-FEM possesses several advantages: (i) insensitive to mesh distortion; (ii) reduce the system stiffness; (iii) convergent and accuracy; (iv) efficient than FEM when the results are at the same accuracy.

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