A hybrid finite element-least square point interpolation method for solving acoustic problems

2012 ◽  
Vol 60 (1) ◽  
pp. 97-112 ◽  
Author(s):  
L. Y. Yao ◽  
D. J. Yu ◽  
W. Y. Cui ◽  
J. W. Zhou
Keyword(s):  
Finite Element ◽  
Interpolation Method ◽  
Least Square ◽  
Hybrid Finite Element ◽  
Point Interpolation Method ◽  
Point Interpolation

Dispersion Error Reduction for Acoustic Problems Using the Finite Element-Least Square Point Interpolation Method

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
L. Y. Yao ◽  
J. W. Zhou ◽  
Z. Zhou ◽  
L. Li
Keyword(s):  
Finite Element ◽  
Interpolation Method ◽  
Local Approximation ◽  
Least Square ◽  
Numerical Dispersion ◽  
Benchmark Problems ◽  
Shape Functions ◽  
Dispersion Error ◽  
Point Interpolation Method ◽  
Point Interpolation

The shape function of the finite element-least square point interpolation method (FE-LSPIM) combines the quadrilateral element for partition of unity and the least square point interpolation method (LSPIM) for local approximation, and inherits the completeness properties of meshfree shape functions and the compatibility properties of FE shape functions, and greatly reduces the numerical dispersion error. This paper derives the formulas and performs the dispersion analysis for the FE-LSPIM. Numerical results for benchmark problems show that, the FE-LSPIM yields considerably better results than the finite element method (FEM) and element-free Galerkin method (EFGM).

The natural neighbor radial point interpolation method in the Elasto-Static analysis of Honeycomb-Shaped foams

2021 ◽  
pp. 2150014
Author(s):  
N. A. Nascimento ◽  
J. Belinha ◽  
R. M. Natal Jorge ◽  
D. E. S. Rodrigues
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Interpolation Method ◽  
The Finite Element Method ◽  
Solid Materials ◽  
Cellular Solid ◽  
Natural Neighbor ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation

Cellular solid materials are progressively becoming more predominant in lightweight structural applications as more technologies realize these materials can be improved in terms of performance, quality control, repeatability and production costs, when allied with fast developing manufacturing technologies such as Additive Manufacturing. In parallel, the rapid advances in computational power and the use of new numerical methods, such as Meshless Methods, in addition to the Finite Element Method (FEM) are highly beneficial and allow for more accurate studies of a wide range of topologies associated with the architecture of cellular solid materials. Since these materials are commonly used as the cores of sandwich panels, in this work, two different topologies were designed — conventional honeycombs and re-entrant honeycombs — for 7 different values of relative density, and tested on the linear-elastic domain, in both in-plane directions, using the Natural Neighbor Radial Point Interpolation Method (NNRPIM), a newly developed meshless method, and the Finite Element Method (FEM) for comparison purposes.

Dynamic analysis of magneto-electro-elastic nanostructures using node-based smoothed radial point interpolation method combined with micromechanics-based asymptotic homogenization technique

2020 ◽  
Vol 31 (20) ◽  
pp. 2342-2361
Author(s):  
Liming Zhou ◽  
Bin Nie ◽  
Chuanxin Ren ◽  
Shuhui Ren ◽  
Guangwei Meng
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Interpolation Method ◽  
Homogenization Method ◽  
Asymptotic Homogenization ◽  
Radial Point Interpolation Method ◽  
Radial Point Interpolation ◽  
Asymptotic Homogenization Method ◽  
Point Interpolation Method ◽  
Point Interpolation

The node-based smoothed radial point interpolation method combined with the asymptotic homogenization method was proposed, as an addition to the finite element method, to address the static and dynamic reactions of magneto-electro-elastic coupling micromechanical problems. First, several basic equations for relevant problems were derived. Second, asymptotic homogenization method was utilized to determine the material properties of magneto-electro-elastic nanomaterials. Third, node-based smoothed radial point interpolation method was applied to obtain the discrete equations of magneto-electro-elastic nanostructures. Then, the Newmark method was introduced to solve the response of microcosmic problems. Finally, several numerical examples were calculated to prove the accuracy, convergence, and reliability of node-based smoothed radial point interpolation method by comparing the results of node-based smoothed radial point interpolation method with those of finite element method.

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