The Effect of Support Domain on Radial Point Interpolation Method (RPIM) for Displacement Analysis in 2D Problem
Abstract
The Radial Point Interpolation Method (RPIM) is one of the Meshfree methods. RPIM approximation function passes through each node point in the influence domain, thus makes the implementation of essential boundary conditions much easier and reducing complexity in numerical algorithms than other Meshfree methods. However, without the use of predefined mesh, there will be considerable differences in the location of the nodes thus causing topological errors. This topological error will create unstable solutions for the simultaneous equations. This present study is concerned with developing a more efficient solution by introducing a support domain in the RPIM. The study is to outline the complete procedures for formulations of RPIM with support domain for two-dimensional plane stress problems and write the corresponding MATLAB source code. The performance of the optimum size of the support domain is evaluated then compare to Finite Element Method (FEM). The result shows that RPIM with support domain, works well and provides an approving comparison against the conventional FEM. The converged solution is achieved.
References
Belytscho, T., Lu, Y.Y. and Gu, L. 1994. Element-free Galerkin methods. Int. J. Numerical. Methods. Engrg, 37, 229-256.
Liu, G.R., and Gu, Y.T. 2005. An introduction to meshfree methods and their programming.
Liu, W. K., Jun, S., Li, S., and Zhang, Y.F. 1995. Reproducing kernel particle methods. Int. J. Numer. Meth. Eng., 20, 1081-1160.
Liu, W. K., Li, S. F., and Belytschko, T. 1997. Moving least-square reproducing kernel methods (I) Methodology and convergence. Comput. Meth. Appl. Mech. Eng., 143, 113–154.
Martinez, J. 2019. Element Free Galerkin (EFG) sensitivity study in structural analysis. Research, Innovation and Development in Engineering. 519 (2019) 012004.
Mokhtaram, M. H., Mohd Noor, M. A., Jamil Abd Nazir, M. Z., Zainal Abidin, A. R., and Mohd Yassin, A. Y. 2020. Enhanced meshfree RPIM with NURBS basis function for analysis of irregular boundary domain. Malaysian Journal of Civil Engineering. 32:1 (2020) 19–27.
Nayroles, B., Touzot, G. and Villon, P. 1992. Generalizing the finite element method: diffuse approximation and diffuse elements. Computational Mechanics, 10, 307-318.
Shaikh, F.U.A. 2012. Role of commercial software in teaching finite element analysis at undergraduate level: A case study. Eng. Educ., vol. 7, no. 2, pp. 2–6.
Wang, J.G., and Liu, G.R. 2002. A point interpolation meshless method based on radial basis functions. Int. J. Numer. Methods Eng., vol. 54, no. 11, pp. 1623–1648.
Wendland, H. 1998. Error estimates for interpolation by compactly supported radial basis functions of minimal degree. J Approximation Theory, 93, 258–396.
Zahiri. S. 2011. Meshfree Methods, in Numerical Analysis - Theory and Application, InTech.
All materials contained within this journal are protected by Intellectual Property Corporation of Malaysia, Copyright Act 1987 and may not be reproduced, distributed, transmitted, displayed, published, or
broadcast without the prior, express written permission of Centre for Graduate Studies, Universiti Selangor, Malaysia. You may not alter or remove any copyright or other notice from copies of this content.
