Hybrid smoothed finite element method for two dimensional acoustic radiation problems

2016 ◽  
Vol 103 ◽  
pp. 90-101 ◽  
Author(s):  
Y.B. Chai ◽  
W. Li ◽  
Z.X. Gong ◽  
T.Y. Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Acoustic Radiation ◽  
Two Dimensional ◽  
Smoothed Finite Element Method ◽  
Element Method

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].

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.

Application of Smoothed Finite Element Method to Two-Dimensional Exterior Problems of Acoustic Radiation

2018 ◽  
Vol 15 (05) ◽  
pp. 1850029 ◽  
Author(s):  
Yingbin Chai ◽  
Zhixiong Gong ◽  
Wei Li ◽  
Tianyun Li ◽  
Qifan Zhang ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Helmholtz Equation ◽  
Numerical Solutions ◽  
Acoustic Radiation ◽  
Unbounded Domains ◽  
Numerical Results ◽  
Smoothed Finite Element Method ◽  
Gradient Smoothing ◽  
Element Method

In this work, the smoothed finite element method using four-node quadrilateral elements (SFEM-Q4) is employed to resolve underwater acoustic radiation problems. The SFEM-Q4 can be regarded as a combination of the standard finite element method (FEM) and the gradient smoothing technique (GST) from the meshfree methods. In the SFEM-Q4, only the values of shape functions (not the derivatives) at the quadrature points are needed and the traditional requirement of coordinate transformation procedure is not necessary to implement the numerical integration. Consequently, no additional degrees of freedom are required as compared with the original FEM. In addition, the original “overly-stiff” FEM model for acoustic problems (governed by the Helmholtz equation) is properly softened due to the gradient smoothing operations implemented over the smoothing domains and the present SFEM-Q4 possesses a relatively appropriate stiffness of the continuous system. Therefore, the well-known numerical dispersion error for Helmholtz equation is decreased significantly and very accurate numerical solutions can be obtained by using relatively coarse meshes. In order to truncate the unbounded domains and employ the domain-based numerical method to tackle the acoustic radiation in unbounded domains, the Dirichlet-to-Neumann (DtN) map is used to ensure that there are no spurious reflections from the far field. The numerical results from several numerical examples demonstrate that the present SFEM-Q4 is quite effective to handle acoustic radiation problems and can produce more accurate numerical results than the standard FEM.

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