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.

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.

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.

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.

scholarly journals An ES-MITC3 Finite Element Method Based on Higher-Order Shear Deformation Theory for Static and Free Vibration Analyses of FG Porous Plates Reinforced by GPLs

2020 ◽  
Vol 2020 ◽  
pp. 1-18 ◽  
Author(s):  
The-Van Tran ◽  
Tuan-Duy Tran ◽  
Quoc Hoa Pham ◽  
Trung Nguyen-Thoi ◽  
Van Ke Tran
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Mass Density ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Dispersion Pattern ◽  
Strain Smoothing ◽  
Triangular Elements ◽  
Element Method

An edge-based smoothed finite element method (ES-FEM) combined with the mixed interpolation of tensorial components technique (MITC) for triangular elements, named as ES-MITC3, was recently proposed to enhance the accuracy of the original MITC3 for analysis of plates and shells. In this study, the ES-MITC3 is extended to the static and vibration analysis of functionally graded (FG) porous plates reinforced by graphene platelets (GPLs). In the ES-MITC3, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains created by two adjacent triangular elements sharing an edge. The effective material properties are variable through the thickness of plates including Young’s modulus estimated via the Halpin–Tsai model and Poisson’s ratio and the mass density according to the rule of mixture. Three types of porosity distributions and GPL dispersion pattern into the metal matrix are examined. Numerical examples are given to demonstrate the performance of the present approach in comparison with other existing methods. Furthermore, the effect of several parameters such as GPL weight fraction, porosity coefficient, porosity distribution, and GPL dispersion patterns on the static and free vibration responses of FG porous plates is discussed in detail.

A cell — based smoothed finite element method for free vibration and buckling analysis of shells

2011 ◽  
Vol 15 (2) ◽  
pp. 347-361 ◽  
Author(s):  
Chien Thai-Hoang ◽  
Nhon Nguyen-Thanh ◽  
Hung Nguyen-Xuan ◽  
Timon Rabczuk ◽  
Stephane Bordas
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Buckling Analysis ◽  
Smoothed Finite Element Method ◽  
A Cell ◽  
Element Method
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