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 com...

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

A truly meshfree method for solving acoustic problems using local weak form and radial basis functions

Application of the edge-based gradient smoothing technique to acoustic radiation and acoustic scattering from rigid and elastic structures in two dimensions

Summary
In this paper, the cell-based Smoothed Finite Element Method (CS-FEM) with the semi-implicit Characteristic-Based Split (CBS) scheme (CBS/CS-FEM) is proposed for computational fluid dynamics (CFD). The 3-node triangular (T3) element and 4-node quadrilateral (Q4) element are employed for present CBS/CS-FEM for two-dimensional flows. The 8-node hexahedral element (H8) is used for three-dimensional flows. Two types of CS-FEM are implemented in this paper. One is standard CS-FEM with quadrilateral gradient smoothing cells for Q4 element and hexahedron cells for H8 element. Another is called as n-sided CS-FEM (nCS-FEM) whose gradient smoothing cells are triangles for Q4 element and pyramids for H8 element. To verify the proposed methods, benchmarking problems are tested for two-dimensional and three-dimensional flows. The benchmarks show that CBS/CS-FEM and CBS/nCS-FEM are capable to solve incompressible laminar flow, and can produce reliable results for both steady and unsteady flows. The proposed CBS/CS-FEM method has merits on better robustness against distorted mesh with only slight more computation time and without losing accuracy, which is important for problems with heavy mesh distortion. The blood flow in carotid bifurcation is also simulated to show capabilities of proposed methods for realistic and complicated flow problems.

A cell-based smoothed finite element method with semi-implicit CBS procedures for incompressible laminar viscous flows

In order to enhance the performance of the discrete shear gap technique (DSG) for shell structures, the coupling of hybrid gradient smoothing technique (H-GST) with DSG using triangular elements (HS-DSG3) is presented to solve the governing partial differential equations of shell structures. In the formulation HS-DSG3, we firstly employ the node-based gradient smoothing technique (N-GST) to obtain the node-based smoothed strain field, then a scale factor α ∈ [ 0 , 1 ] is used to reconstruct a new strain field which includes both the strain components from standard DGS3 and the strain components from node-based smoothed DSG3 (NS-DSG3). The HS-DSG3 takes advantage of the “overly-soft” NS-DSG3 model and the “overly-stiff” DSG3 model, and has a relatively appropriate stiffness of the continuous system. Therefore, the degree of the solution accuracy can be improved significantly. Several typical benchmark numerical examples have been investigated and it is demonstrated that the present HS-DSG3 can provide better numerical solutions than the original DSG3 for shell structures.

Hybrid gradient smoothing technique with discrete shear gap method for shell structures

The smoothed finite element method (S-FEM) has been recently developed as an effective solver for solid mechanics problems. This paper represents an effective approach to compute the lower bounds of vibration modes or eigenvalues of elasto-dynamic problems, by making use of the important softening effects of node-based S-FEM (NS-FEM). We first use NS-FEM, FEM and the analytic approach to compute the eigenvalues of transverse free vibration in strings and membranes. It is found that eigenvalues by NS-FEM are always smaller than those by FEM and the analytic method. However, NS-FEM produces spurious unphysical modes because of overly soft behavior. A technique is then proposed to remove them by analyzing their vibration shapes (eigenvectors). It is observed that spurious modes with excessively large wave numbers, which are unrelated to the physical deflection shapes but related to the discretization density, therefore can be easily removed. The final results of NS-FEM become the lower bound of eigenvalues and the accuracy can be improved via mesh refinement. And NS-FEM solutions (softer) are more reliable, because the large wave number component can be used as an indicator, which is available in FEM (stiffer), on the quality of the numerical solutions. The proposed NS-FEM procedure offers a viable and practical computational means to effectively compute the lower bounds of eigenvalues for solid mechanics problems.

Lower Bound of Vibration Modes Using the Node-Based Smoothed Finite Element Method (NS-FEM)

This paper represents some basic mathematic theories for Gs spaces of functions that can be used for weakened weak (W2) formulations, upon which the smoothed finite element methods (S-FEMs) and the smoothed point interpolation methods (S-PIMs) are based for solving mechanics problems. We first introduce and prove properties of Gs spaces, such as the lower boundedness and convergence of the norms, which are in contrast with H1 spaces. We then prove the equivalence of the Gs norms and its corresponding semi-norms. These mathematic theories are important and essential for the establishment of theoretical frame and the development of relevant numerical approaches. Finally, numerical examples are presented by using typical S-FEM models known as the NS-FEM and αS-FEM to examine the properties of a smoothed method based on Gs spaces, in comparison with the standard FEM with weak formulation.

Meng Chen

Papers

Lower Bound of Vibration Modes Using the Node-Based Smoothed Finite Element Method (NS-FEM)

Mathematical Basis of G Spaces