A Two-Step Taylor Galerkin Smoothed Finite Element Method for Lagrangian Dynamic Problem

2015 ◽  
Vol 12 (04) ◽  
pp. 1540004 ◽  
Author(s):  
Xiang Yang Cui ◽  
Shu Chang ◽  
Guang Yao Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Weak Form ◽  
Two Dimensional ◽  
Mesh Distortion ◽  
Smoothed Finite Element Method ◽  
System Equations ◽  
The Stability ◽  
Lagrangian Dynamic ◽  
Element Method

In this paper, a two-step Taylor Galerkin smoothed finite element method (TG-SFEM) is presented to deal with the two-dimensional Lagrangian dynamic problems. In this method, the smoothed Galerkin weak form is employed to create discretized system equations, and the cell-based smoothing domains are used to perform the smoothing operation and the numerical integration. The stability and the adaptation of elements aberrations presented in the two-step TG-SFEM are studied through detailed analyses of numerical examples. In the analysis of wave propagation, the proposed method can provide smoother displacement and stress than the common SFEM does, and energy fluctuations are found to be minimal. In the large deformation problems, the TG-SFEM can acclimatize itself to the mesh distortion effectively and stay bounded for long durations because the isoparametric elements are replaced, and area integration over each smoothing cells is recast into line integration along edges and no mapping is needed. Therefore, the stability, flexibility of elements distortion and the property of energy conservation of the TG-SFEM applied on two-dimensional solid problems are well represented and clarified.

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].

THERMO-MECHANICAL ANALYSES OF COMPOSITE STRUCTURES USING FACE-BASED SMOOTHED FINITE ELEMENT METHOD

2014 ◽  
Vol 06 (02) ◽  
pp. 1450020 ◽  
Author(s):  
SHIZHE FENG ◽  
XIANGYANG CUI ◽  
GUANGYAO LI
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Composite Structures ◽  
Weak Form ◽  
Tetrahedral Mesh ◽  
The Face ◽  
Smoothed Finite Element Method ◽  
System Equations ◽  
Transient Thermal ◽  
Element Method

A face-based smoothed finite element method (FS-FEM) is extended to deal with the transient thermal mechanical analyses of composite structures. For this method, the problem domain is first discretized into a set of tetrahedral elements, and the face-based smoothing domains are further formed along the faces of the tetrahedral meshes. The smoothed Galerkin weak form is employed to obtain discretized system equations, and the face-based smoothing domains are used to perform the smoothing operation. After applying these approaches, the numerical integration becomes a simple summation over each smoothing domain. Several composite structures with different kinds of boundary conditions are studied in this paper. Compared with the 4-node tetrahedral FEM, the FS-FEM can achieve much better accuracy and higher convergence when using the same tetrahedral mesh.

A Stabilized Finite Element Method for Non-Stationary Conduction-Convection Problems

2011 ◽  
Vol 3 (2) ◽  
pp. 239-258 ◽  
Author(s):  
Ke Zhao ◽  
Yinnian He ◽  
Tong Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Optimal Error Estimates ◽  
Two Dimensional ◽  
Element Level ◽  
Optimal Error ◽  
Stabilized Finite Element ◽  
Stabilized Finite Element Method ◽  
The Stability ◽  
Element Method

AbstractThis paper is concerned with a stabilized finite element method based on two local Gauss integrations for the two-dimensional non-stationary conduction-convection equations by using the lowest equal-order pairs of finite elements. This method only offsets the discrete pressure space by the residual of the simple and symmetry term at element level in order to circumvent the inf-sup condition. The stability of the discrete scheme is derived under some regularity assumptions. Optimal error estimates are obtained by applying the standard Galerkin techniques. Finally, the numerical illustrations agree completely with the theoretical expectations.

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.

Sign in / Sign up

Export Citation Format

Share Document