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.

A LINEARLY CONFORMING RADIAL POINT INTERPOLATION METHOD FOR SOLID MECHANICS PROBLEMS

2006 ◽  
Vol 03 (04) ◽  
pp. 401-428 ◽  
Author(s):  
G. R. LIU ◽  
Y. LI ◽  
K. Y. DAI ◽  
M. T. LUAN ◽  
W. XUE
Keyword(s):  
Solid Mechanics ◽  
Interpolation Method ◽  
Weak Form ◽  
Delta Function ◽  
Field Function ◽  
Radial Point Interpolation Method ◽  
Radial Point Interpolation ◽  
Integration Techniques ◽  
Point Interpolation Method ◽  
Point Interpolation

A linearly conforming radial point interpolation method (LC-RPIM) is presented for stress analysis of two-dimensional solids. In the LC-RPIM method, each field node is enclosed by a Voronoi polygon, and the displacement field function is approximated using RPIM shape functions of Kronecker delta function property created by simple interpolation using local nodes and radial basis functions augmented with linear polynomials to guarantee linear consistency. The system equations are then derived using the Galerkin weak form and nodal integration techniques, and the essential boundary conditions are imposed directly as in the finite element method. The LC-RPIM method is verified via various numerical examples and an extensive comparison study is conducted with the conventional RPIM, analytical approach and FEM. It is found that the presented LC-RPIM is more stable, more accurate in stress and more efficient than the conventional RPIM.

Shear Locking Analysis of Plate Bending by Using Meshless Local Radial Point Interpolation Method

2012 ◽  
Vol 166-169 ◽  
pp. 2867-2870 ◽  
Author(s):  
Ping Xia ◽  
Ke Xiang Wei
Keyword(s):  
Boundary Conditions ◽  
Interpolation Method ◽  
Delta Function ◽  
Plate Bending ◽  
Shear Locking ◽  
Radial Point Interpolation Method ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Two Sides

The shape function of the meshless local radial point interpolation method is constructed by using the radial basis functions and possesses Kronecker delta function properties. Therefore, the essential boundary conditions can be easily imposed. Causation of shear locking occur in plate bending is analyzed. Bending problems for plate with two sides simply supported, the other two sides clamped boundary conditions, are analyzed by the meshless local radial point interpolation method. The shear locking is easier avoided in the meshless method than in the finite element method, and the measure of avoiding the shear locking are presented.

ANALYSIS OF MINDLIN–REISSNER PLATES USING CELL-BASED SMOOTHED RADIAL POINT INTERPOLATION METHOD

2010 ◽  
Vol 02 (03) ◽  
pp. 653-680 ◽  
Author(s):  
X. Y. CUI ◽  
G. R. LIU ◽  
G. Y. LI
Keyword(s):  
Plate Theory ◽  
Interpolation Method ◽  
Free Vibration Analysis ◽  
Delta Function ◽  
Shear Locking ◽  
Radial Point Interpolation Method ◽  
First Order ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation

In this paper, a formulation for the static and free vibration analysis of Mindlin–Reissner plates is proposed using the cell-based smoothed radial point interpolation method (CS-RPIM) with sub-domain smoothing operations. The radial basis functions augmented with polynomial basis are employed to construct the shape functions that have the Delta function property. The generalized smoothed Galerkin (GS-Galerkin) weakform is adopted to discretize the governing differential equations, and the curvature smoothing is performed to relax the continuity requirement and to improve the accuracy and the rate of convergence of the solution. The present CS-RPIM formulation is based on the first-order shear deformation plate theory, with effective treatment for shear-locking and hence is applicable to both thin and relatively thick plates. To verify the accuracy and stability of the present formulation, intensive comparison studies are conducted with existing results available in the literature and good agreements are obtained. The numerical examples confirm that the present method is shear-locking free and very stable and accurate even using extremely distributed nodes.

A Local Radial Point Interpolation Method for Two-Dimensional Schrödinger Equation

2012 ◽  
Vol 268-270 ◽  
pp. 1888-1893
Author(s):  
Wei Gang Zhai ◽  
Xing Hui Cai ◽  
Jiang Ren Lu ◽  
Xin Li Sun
Keyword(s):  
Schrödinger Equation ◽  
Analytical Solutions ◽  
Schrodinger Equation ◽  
Interpolation Method ◽  
Weak Form ◽  
Time Dependent ◽  
Radial Point Interpolation Method ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation

A local radial point interpolation method is employed to the simulation of the time dependent Schrödinger equation with arbitrary potential function. Local weak form of the time dependent Schrödinger equation is obtained and radial point interpolation shape functions are applied in the space discretization. Computations are carried out for an example of time dependent Schrödinger equation having analytical solutions. Numerical results agreed with analytical solutions very well.

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