A cell‐based smoothed radial point interpolation method with virtual nodes for three‐dimensional mid‐frequency acoustic problems

2019 ◽  
Vol 119 (6) ◽  
pp. 548-566 ◽  
Author(s):  
Guiyong Zhang ◽  
Zecong Chen ◽  
Zhixiang Sui ◽  
Dongsong Tao ◽  
Zhicheng He ◽  
...  
Keyword(s):  
Interpolation Method ◽  
Three Dimensional ◽  
Radial Point Interpolation Method ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
A Cell ◽  
Point Interpolation

MESHFREE ELASTODYNAMIC ANALYSIS OF THREE-DIMENSIONAL SOLIDS USING RADIAL POINT INTERPOLATION METHOD

2011 ◽  
Vol 02 (01) ◽  
pp. 83-95 ◽  
Author(s):  
KYOKO HASEGAWA ◽  
SUSUMU NAKATA ◽  
SATOSHI TANAKA
Keyword(s):  
Stiffness Matrix ◽  
Interpolation Method ◽  
Three Dimensional ◽  
Time Dependent ◽  
Partial Differential ◽  
Radial Point Interpolation Method ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Matrix Construction

Meshfree methods are effective tools for solving partial differential equations. The radial point interpolation method, a partial differential equation solver based on a meshfree approach, enables accurate imposition of displacement boundary conditions and has been successfully applied to elastostatic analysis of various kinds of three-dimensional solids. In this method, stiffness matrix construction accounts for the majority of CPU time required for the entire process, resulting in high computational costs, especially when higher-order numerical integration is applied for accurate matrix construction. An alternative method, modified radial point interpolation, was proposed to overcome this shortcoming and has accomplished fast computation of elastostatic solid analysis. The purpose of this study is to develop an algorithm for time-dependent simulation of three-dimensional elastic solids. We show that the modified radial point interpolation method also accelerates the construction of the mass matrix required for time-dependent analysis in addition to that of the stiffness matrix. In our approach, the problem domain is assumed to have an implicit function representation that can be constructed from a set of surface points measured using a three-dimensional scanning system. Several numerical tests for elastodynamic analysis of complex shape models are presented.

Analysis of Transient Thermo-Elastic Problems Using a Cell-Based Smoothed Radial Point Interpolation Method

2016 ◽  
Vol 13 (05) ◽  
pp. 1650023 ◽  
Author(s):  
Gang Wu ◽  
Jian Zhang ◽  
Yuelin Li ◽  
Lairong Yin ◽  
Zhiqiang Liu
Keyword(s):  
Transfer Problem ◽  
Interpolation Method ◽  
Weak Form ◽  
Delta Function ◽  
Radial Point Interpolation Method ◽  
Kronecker Delta ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
A Cell ◽  
Point Interpolation

The transient thermo-elastic problems are solved by a cell-based smoothed radial point interpolation method (CS-RPIM). For this method, the problem domain is first discretized using triangular cells, and each cell is further divided into smoothing cells. The field functions are approximated using RPIM shape functions which have Kronecker delta function property. The system equations are derived using the generalized smoothed Galerkin (GS-Galerkin) weak form. At first, the temperature field is acquired by solving the transient heat transfer problem and it is then employed as an input for the mechanical problem to calculate the displacement and stress fields. Several numerical examples with different kinds of boundary conditions are investigated to verify the accuracy, convergence rate and stability of the present method.

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