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

A cell-based smoothed finite element method for three dimensional solid structures

2012 ◽  
Vol 16 (7) ◽  
pp. 1230-1242 ◽  
Author(s):  
Hung Nguyen-Xuan ◽  
Hiep Vinh Nguyen ◽  
Stephane Bordas ◽  
Timon Rabczuk ◽  
Marc Duflot
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
Smoothed Finite Element Method ◽  
A Cell ◽  
Element Method

scholarly journals A Stochastic Galerkin Cell-based Smoothed Finite Element Method (SGCS–FEM)

2019 ◽  
Vol 17 (08) ◽  
pp. 1950054
Author(s):  
Tittu Varghese Mathew ◽  
Lars Beex ◽  
Stéphane PA Bordas ◽  
Sundararajan Natarajan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Numerical Study ◽  
Mesh Size ◽  
Statistical Characteristics ◽  
Smoothed Finite Element Method ◽  
Element Method

In this paper, the cell-based smoothed finite element method is extended to solve stochastic partial differential equations with uncertain input parameters. The spatial field of Young’s Modulus and the corresponding stochastic results are represented by Karhunen-Loéve expansion and polynomial chaos expansion, respectively. Young’s Modulus of structure is considered to be random for stochastic static as well as free vibration problems. Mathematical expressions and the solution procedure are articulated in detail to evaluate the statistical characteristics of responses in terms of the static displacements and the free vibration frequencies. The feasibility and the effectiveness of the proposed SGCS–FEM method in terms of accuracy and lower demand on the mesh size in the solution domain over that of conventional FEM for stochastic problems are demonstrated by carefully chosen numerical examples. From the numerical study, it is inferred that the proposed framework yields accurate results.

scholarly journals On stabilization of the node-based smoothed finite element method for free vibration problems

2010 ◽  
Vol 32 (3) ◽  
pp. 167-181
Author(s):  
Bui Xuan Thang ◽  
Nguyen Xuan Hung ◽  
Ngo Thanh Phong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Solid Mechanics ◽  
High Reliability ◽  
Free Vibration Analysis ◽  
Zero Energy ◽  
Computational Effect ◽  
Smoothed Finite Element Method ◽  
Element Method

The node-based smoothed finite element method (NS-FEM) has been recently proposed by Liu et al to enhance the computational effect for solid mechanics problems. However, it is evident that the NS-FEM behaves "overly-soft" and so it may lead to instability for dynamic problems. The instability can be clearly shown as spurious non-zero energy modes in free vibration analysis. In this paper, we present a stabilization of the node-based smoothed finite element method (SN-FEM) that is stable (no spurious non-zero energy modes) and more effective than the standard finite element method (FEM). Three numerical illustrations are given to evince the high reliability of the proposed formulation.

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.

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