A truly mesh‐distortion‐enabled implementation of cell‐based smoothed finite element method for incompressible fluid flows with fixed and moving boundaries

2020 ◽  
Vol 121 (14) ◽  
pp. 3227-3248 ◽  
Author(s):  
Tao He
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Incompressible Fluid ◽  
Fluid Flows ◽  
Moving Boundaries ◽  
Mesh Distortion ◽  
Smoothed Finite Element Method ◽  
Incompressible Fluid Flows ◽  
Element Method

Semi-Implicit Coupling of CS-FEM and FEM for the Interaction Between a Geometrically Nonlinear Solid and an Incompressible Fluid

2015 ◽  
Vol 12 (05) ◽  
pp. 1550025 ◽  
Author(s):  
Tao He
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Incompressible Fluid ◽  
Computational Cost ◽  
Geometrically Nonlinear ◽  
Arbitrary Lagrangian Eulerian ◽  
Coupling Strategy ◽  
Smoothed Finite Element Method ◽  
Characteristic Based Split ◽  
Element Method

A semi-implicit coupling strategy under the arbitrary Lagrangian–Eulerian description is presented for the incompressible fluid flow past a geometrically nonlinear solid in this paper. The incompressible fluid is solved by means of the characteristic-based split (CBS) finite element method while the cell-based smoothed finite element method is employed to settle the governing equation of the geometrically nonlinear solid. Because of the CBS fluid solver, the present coupling strategy is performed in a semi-implicit fashion. In particular, the first step of the CBS scheme is explicitly treated whereas the others are implicitly coupled with the structural motion. The computational cost is hence reduced because no subiterations are included in the explicit coupling step and the fluid mesh is frozen in the implicit coupling step. A classic cantilever problem is dealt with to validate the structural solver, and then flow-induced vibrations of a restrictor flap in a uniform channel flow is analyzed in detail. The obtained results agree well with the existing data.

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].

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.

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.

An ABAQUS Implementation of the Cell-Based Smoothed Finite Element Method (CS-FEM)

2019 ◽  
Vol 17 (02) ◽  
pp. 1850127 ◽  
Author(s):  
X. Cui ◽  
X. Han ◽  
S. Y. Duan ◽  
G. R. Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Software Package ◽  
Strain Energy ◽  
Computational Accuracy ◽  
Mesh Distortion ◽  
Processing Program ◽  
Smoothed Finite Element Method ◽  
Solution Accuracy ◽  
Element Method

The smoothed finite element method (S-FEM) has been developed recent years and is increasingly used for stress analysis for engineering design of structures, due to its high computational accuracy and outstanding robustness in against mesh distortion. However, there is currently no commercial S-FEM software package available for convenient engineering applications. This paper aims to integrate S-FEM into the [Formula: see text] software, because it is most widely used in engineering analyses and well integrated in computer aided engineering (CAE). From a family of S-FEM models, the cell-based finite element method (CS-FEM) is chosen to be implemented in ABAQUS, because a smoothing cell in the CS-FEM involves only one element, and hence the implementation can be achieved via the use of the user-defined element library (UEL). Since only nodal displacement results can be extracted when UEL subroutine is used in ABAQUS, a post-processing program is also developed to compute nodal strains/stresses and strain energy results that are useful in structure analysis and CAE. Our CS-FEM UEL is validated using four numerical examples under plane stress conditions. Compared with standard ABAQUS, the CS-FEM in ABAQUS improves the solution accuracy remarkably, and we have also confirmed the robustness of CS-FEM against heavily distorted meshes.

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