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.

An Efficient Cell-Based Smoothed Finite Element Method for Free Vibrations of Magneto-Electro-Elastic Beams

2019 ◽  
Vol 17 (04) ◽  
pp. 1950001 ◽  
Author(s):  
Liming Zhou ◽  
Shuhui Ren ◽  
Yan Cai ◽  
Feng Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Coupling Effect ◽  
Magnetic Coupling ◽  
Free Vibrations ◽  
Fe Model ◽  
The Finite Element Method ◽  
Smoothed Finite Element Method ◽  
Gradient Smoothing ◽  
Element Method

Magneto-electro-elastic (MEE) materials are widely used in intelligent structure systems owing to their electronic, mechanical and magnetic coupling effects. To overcome the over-stiffness of the finite element method (FEM) stiffness matrix and simulate the free vibration of MEE structures more accurately, we introduced the gradient smoothing technique into MEE multi-physical-field FE model and thereby deduced the cell-based smoothed finite element method (CS-FEM) equations of MEE materials. The MEE beams and layered beam affected by the coupling effect of multiple physical fields under different boundary conditions were computed by CS-FEM, after comparing results with those of FEM and reference solutions, the accuracy and efficiency of CS-FEM were validated.

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.

A GENERALIZED GRADIENT SMOOTHING TECHNIQUE AND THE SMOOTHED BILINEAR FORM FOR GALERKIN FORMULATION OF A WIDE CLASS OF COMPUTATIONAL METHODS

2008 ◽  
Vol 05 (02) ◽  
pp. 199-236 ◽  
Author(s):  
G. R. LIU
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Bilinear Form ◽  
Interpolation Method ◽  
Smoothing Technique ◽  
Generalized Gradient ◽  
Gradient Smoothing Technique ◽  
Smoothed Finite Element Method ◽  
Gradient Smoothing ◽  
Element Method

This paper presents a generalized gradient smoothing technique, the corresponding smoothed bilinear forms, and the smoothed Galerkin weakform that is applicable to create a wide class of efficient numerical methods with special properties including the upper bound properties. A generalized gradient smoothing technique is first presented for computing the smoothed strain fields of displacement functions with discontinuous line segments, by "rudely" enforcing the Green's theorem over the smoothing domain containing these discontinuous segments. A smoothed bilinear form is then introduced for Galerkin formulation using the generalized gradient smoothing technique and smoothing domains constructed in various ways. The numerical methods developed based on this smoothed bilinear form will be spatially stable and convergent and possess three major important properties: (1) it is variationally consistent, if the solution is sought in a Hilbert space; (2) the stiffness of the discretized model will be reduced compared to the model of the finite element method (FEM) and often the exact model, which allows us to obtain upper bound solutions with respect to both the FEM solution and the exact solution; (3) the solution of the numerical method developed using the smoothed bilinear form is less insensitive to the quality of the mesh, and triangular meshes can be used perfectly without any problems. These properties have been proved, examined, and confirmed by the numerical examples. The smoothed bilinear form establishes a unified theoretical foundation for a class of smoothed Galerkin methods to analyze solid mechanics problems for solutions of special and unique properties: the node-based smoothed point interpolation method (NS-PIM), smoothed finite element method (SFEM), node-based smoothed finite element method (N-SFEM), edge-based smoothed finite element method (E-SFEM), cell-based smoothed point interpolation method (CS-PIM), etc.

scholarly journals Smoothed finite element method for two-dimensional elasto-plasticity

2009 ◽  
Vol 31 (3-4) ◽  
Author(s):  
Stéphane Pierre Alain Bordascorres ◽  
Hung Nguyen-Dang ◽  
Quyen Phan-Phuong ◽  
Hung Nguyen-Xuan ◽  
Sundararajan Natarajan ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Two Dimensional ◽  
Fe Method ◽  
Mesh Distortion ◽  
Elasto Plasticity ◽  
Smoothed Finite Element Method ◽  
Displacement Based ◽  
Theoretical Developments ◽  
Element Method

This communication shows how the smoothed finite element method (SFEM) very recently proposed by G. R. Liu [14] can be extended to elasto-plasticity. The SFEM results are in excellent agreement with the finite element (FEM) and analytical results. For the examples treated, the method is quite insensitive to mesh distortion and volumetric locking. Moreover, the SFEM yields more compliant load-displacement curves compared to the standard, displacement based FE method, as expected from the theoretical developments recently published in [4], [3] and [6].

Edge-Based Smoothed Finite Element Method Using Two-Step Taylor Galerkin Algorithm for Lagrangian Dynamic Problems

2015 ◽  
Vol 12 (05) ◽  
pp. 1550028 ◽  
Author(s):  
Xiangyang Cui ◽  
Shu Chang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Long Time ◽  
Smoothed Finite Element Method ◽  
Linear Elements ◽  
Edge Based ◽  
Gradient Smoothing ◽  
Solid Dynamics ◽  
Dynamics Problems ◽  
Element Method

An edge-based smoothed finite element method (ESFEM) using two-step Taylor Galerkin (TS-TG) algorithm is formulated for two-dimensional solid dynamics problems using linear elements. Although explicit method with classical displacement formulations is the traditional way to simulate fast impact, errors accumulate rapidly resulted from mass, momentum or energy nonconservation. The proposed method is momentum conservative so that energy fluctuations can be minimal and stay bounded for long time. In the present method, the problem areas are firstly discretized into a series of triangular cells, and edge-based smoothing domains are further formed associated with the cell edges. The strain field using the gradient smoothing technique over each smoothing domain is smoothed, which is used for performing the numerical integration. The triangular elements using ESFEM can work for extremely distorted meshes. The newly proposed method can present a good property of accuracy and conservation for a long time.

An Edge-Based Smoothed Finite Element Method for Analyzing Stiffened Plates

2019 ◽  
Vol 16 (06) ◽  
pp. 1840031 ◽  
Author(s):  
Wei Li ◽  
Yingbin Chai ◽  
Xiangyu You ◽  
Qifan Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Sound Radiation ◽  
Stiffened Plates ◽  
Smoothing Technique ◽  
Gradient Smoothing Technique ◽  
Smoothed Finite Element Method ◽  
Edge Based ◽  
Gradient Smoothing ◽  
Element Method

In this paper, an edge-based smoothed finite element method with the discrete shear gap using triangular elements (ES-DSG3) is presented for static, free vibration and sound radiation analyses of plates stiffened by eccentric and concentric stiffeners. In the present model, the ES-DSG3 for the plate element with the isoparametric thick-beam element is employed to formulate stiffened plate structures. The deflections and rotations of the plates and the stiffeners are connected at tying positions. By using Rayleigh integral, sound radiation of stiffened plates subjected to a point load can be obtained. The edge-based gradient smoothing technique is employed to perform the related numerical integrations over the edge-based smoothing domains. Compared with the original DSG3 model, the present ES-DSG3 model is relatively softer as a result of the edge-based gradient smoothing technique. From several numerical examples, it is observed that the ES-DSG3 can produce more accurate numerical solutions than the original DSG3 for stiffened plates.

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