Factors affecting accuracy of radial point interpolation meshfree method for 3-D solid mechanics

2013 ◽  
Vol 20 (11) ◽  
pp. 3229-3246 ◽  
Author(s):  
Chong Peng ◽  
Hui-na Yuan ◽  
Bing-yin Zhang ◽  
Yan Zhang
Keyword(s):  
Solid Mechanics ◽  
Meshfree Method ◽  
Factors Affecting ◽  
Radial Point Interpolation ◽  
Point Interpolation

MESHFREE CELL-BASED SMOOTHED ALPHA RADIAL POINT INTERPOLATION METHOD (CS-α RPIM) FOR SOLID MECHANICS PROBLEMS

2013 ◽  
Vol 10 (04) ◽  
pp. 1350020 ◽  
Author(s):  
G. R. LIU ◽  
G. Y. ZHANG ◽  
Z. ZONG ◽  
M. LI
Keyword(s):  
Solid Mechanics ◽  
Interpolation Method ◽  
Shape Functions ◽  
Radial Point Interpolation Method ◽  
Practical Procedure ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Factor Α ◽  
2D And 3D

This paper presents a novel and effective cell-based smoothed alpha radial point interpolation method (CS-αRPIM) using αPIM shape functions for approximating displacement and cell-based smoothed strains for displacement gradient construction. Using a scaling factor α ∈ [0, 1], the αPIM shape functions are combinations of the condensed RPIM (RPIM-Cd) shape functions and the linear PIM shape functions, where the former often leads to a "softer" CS-RPIM model, and the latter a "stiffer" linear CS-RPIM model (which is as same as linear FEM), compared to the exact one. Through adjusting the value of α in our new CS-αRPIM, the stiffness of the model can be "designed" for desired purposes, such as for seeking nearly exact solutions in strain energy norm (or possibly other norms). A simple and practical procedure to search for such an α has also been presented. Some 2D and 3D numerical examples are studied to examine various properties of the present method in terms of accuracy, convergence and computational efficiency.

Using Meshfree Weak-Strong Form Method for a 2-D Heat Transfer Problem

2009 ◽  
Author(s):  
S. Zahiri ◽  
F. Daneshmand ◽  
M. H. Akbari
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Transfer Problem ◽  
Interpolation Method ◽  
Meshfree Method ◽  
Weak Form ◽  
Heat Transfer Problem ◽  
Radial Point Interpolation ◽  
Point Interpolation ◽  
Local Weak Form

In this work, the numerical simulation of 2-D heat transfer problem is studied by using a meshfree method. The method is based on the local weak form collocation and the meshfree weak-strong (MWS) form. The goal of the paper is to find the temperature distribution in a rectangular plate. The results obtained are compared by those obtained by use of other numerical methods. Two types of boundary conditions are considered in this paper: Dirichlet and Neumann types. The Local Radial Point Interpolation Method (LRPIM) is used as the meshfree method. It is shown that the essential boundary conditions can be easily enforced as in the Finite Element Method (FEM), since the radial point interpolation shape functions posses the Kronecker delta property. It is also shown that the natural (derivative) boundary conditions can be satisfied by using the MWS method and no additional equation or treatment are needed. The MWS method as presented in this paper works well with local quadrature cells for nodes on the natural boundary and can be generated without any difficulty.

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.

Radial point interpolation collocation method based approximation for 2D fractional equation models

2021 ◽  
Vol 97 ◽  
pp. 153-161
Author(s):  
Qingxia Liu ◽  
Pinghui Zhuang ◽  
Fawang Liu ◽  
Minling Zheng ◽  
Shanzhen Chen
Keyword(s):  
Collocation Method ◽  
Radial Point Interpolation ◽  
Point Interpolation ◽  
Fractional Equation

Simulation of the viscoplastic extrusion process using the radial point interpolation meshless method

2021 ◽  
pp. 146442072098858
Author(s):  
ROSS Costa ◽  
J Belinha ◽  
RM Natal Jorge ◽  
DES Rodrigues
Keyword(s):  
Meshless Method ◽  
Fused Deposition Modeling ◽  
Interpolation Method ◽  
Extrusion Process ◽  
Fused Deposition ◽  
Radial Point Interpolation ◽  
Large Growth ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Deposition Modeling

Additive manufacturing is an emergent technology, which witnessed a large growth demanded by the consumer market. Despite this growth, the technology needs scientific regulation and guidelines to be reliable and consistent to the point that is feasible to be used as a source of manufactured end-products. One of the processes that has seen the most significant development is the fused deposition modeling, more commonly known as 3D printing. The motivation to better understand this process makes the study of extrusion of materials important. In this work, the radial point interpolation method, a meshless method, is applied to the study of extrusion of viscoplastic materials, using the formulation originally intended for the finite element method, the flow formulation. This formulation is based on the reasoning that solid materials under those conditions behave like non-Newtonian fluids. The time stepped analysis follows the Lagrangian approach taking advantage of the easy remeshing inherent to meshless methods. To validate the newly developed numerical tool, tests are conducted with numerical examples obtained from the literature for the extrusion of aluminum, which is a more common problem. Thus, after the performed validation, the algorithm can easily be adapted to simulate the extrusion of polymers in fused deposition modeling processes.

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