A meshless Reissner plate bending procedure using local radial point interpolation with an efficient integration scheme

2019 ◽  
Vol 99 ◽  
pp. 46-59 ◽  
Author(s):  
D.H. Konda ◽  
J.A.F. Santiago ◽  
J.C.F. Telles ◽  
J.P.F. Mello ◽  
E.G.A. Costa
Keyword(s):  
Integration Scheme ◽  
Plate Bending ◽  
Reissner Plate ◽  
Radial Point Interpolation ◽  
Efficient Integration ◽  
Point Interpolation

scholarly journals FE-Meshfree QUAD4 Element with Modified Radial Point Interpolation Function for Structural Dynamic Analysis

2019 ◽  
Vol 2019 ◽  
pp. 1-23 ◽  
Author(s):  
Hongjun Zhang ◽  
Guangsong Chen ◽  
Linfang Qian ◽  
Jia Ma
Keyword(s):  
Forced Vibration ◽  
Vibration Analysis ◽  
Numerical Solutions ◽  
Integration Scheme ◽  
Interpolation Function ◽  
Shape Functions ◽  
Structural Dynamic ◽  
Radial Point Interpolation ◽  
Point Interpolation ◽  
Forced Vibration Analysis

The partition-of-unity method based on FE-Meshfree QUAD4 element synthesizes the respective advantages of meshfree and finite element methods by exploiting composite shape functions to obtain high-order global approximations. This method yields high accuracy and convergence rate without necessitating extra nodes or DOFs. In this study, the FE-Meshfree method is extended to the free and forced vibration analysis of two-dimensional solids. A modified radial point interpolation function without any supporting tuning parameters is applied to construct the composite shape functions. The governing equations of elastodynamic problem are transformed into a standard weak formulation and then discretized into time-dependent equations which are solved via Bathe time integration scheme to conduct the forced vibration analysis. Several numerical test problems are solved and compared against previously published numerical solutions. Results show that the proposed FE-Meshfree QUAD4 element owns greater tolerance for mesh distortion and provides more accurate solutions.

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.

scholarly journals On the Factors Affecting the Accuracy and Robustness of Smoothed-Radial Point Interpolation Method

2016 ◽  
Vol 9 (1) ◽  
pp. 43-72 ◽  
Author(s):  
Abderrachid Hamrani ◽  
Idir Belaidi ◽  
Eric Monteiro ◽  
Philippe Lorong
Keyword(s):  
Radial Basis Functions ◽  
Interpolation Method ◽  
Basis Functions ◽  
Integration Scheme ◽  
Shape Parameters ◽  
Radial Point Interpolation Method ◽  
Radial Point Interpolation ◽  
Radial Basis ◽  
Point Interpolation Method ◽  
Point Interpolation

AbstractIn order to overcome the possible singularity associated with the Point Interpolation Method (PIM), the Radial Point Interpolation Method (RPIM) was proposed by G. R. Liu. Radial basis functions (RBF) was used in RPIM as basis functions for interpolation. All these radial basis functions include shape parameters. The choice of these shape parameters has been and stays a problematic theme in RBF approximation and interpolation theory. The object of this study is to contribute to the analysis of how these shape parameters affect the accuracy of the radial PIM. The RPIM is studied based on the global Galerkin weak form performed using two integration technics: classical Gaussian integration and the strain smoothing integration scheme. The numerical performance of this method is tested on their behavior on curve fitting, and on three elastic mechanical problems with regular or irregular nodes distributions. A range of recommended shape parameters is obtained from the analysis of different error indexes and also the condition number of the matrix system. All resulting RPIM methods perform very well in term of numerical computation. The Smoothed Radial Point Interpolation Method (SRPIM) shows a higher accuracy, especially in a situation of distorted node scheme.

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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