Mesh Free Radial Point Interpolation Based Displacement Recovery Techniques for Elastic Finite Element Analysis

Mohd. Ahmed, Devinder Singh, Saeed AlQadhi and Majed A. Alrefae
Additional contact information
Mohd. Ahmed: Civil Engineering Department, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia
Devinder Singh: State Insurance Corporation, New Delhi 110077, India
Saeed AlQadhi: Civil Engineering Department, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia
Majed A. Alrefae: Mechanical Engineering Department, Royal Commission of Jubail & Yanbu, Yanbu 41912, Saudi Arabia

Mathematics, 2021, vol. 9, issue 16, 1-19

Abstract: The study develops the displacement error recovery method in a mesh free environment for the finite element solution employing the radial point interpolation (RPI) technique. The RPI technique uses the radial basis functions (RBF), along with polynomials basis functions to interpolate the displacement fields in a node patch and recovers the error in displacement field. The global and local errors are quantified in both energy and L 2 norms from the post-processed displacement field. The RPI technique considers multi-quadrics/gaussian/thin plate splint RBF in combination with linear basis function for displacement error recovery analysis. The elastic plate examples are analyzed to demonstrate the error convergence and effectivity of the RPI displacement recovery procedures employing mesh free and mesh dependent patches. The performance of a RPI-based error estimators is also compared with the mesh dependent least square based error estimator. The triangular and quadrilateral elements are used for the discretization of plates domains. It is verified that RBF with their shape parameters, choice of elements, and errors norms influence considerably on the RPI-based displacement error recovery of finite element solution. The numerical results show that the mesh free RPI-based displacement recovery technique is more effective and achieve target accuracy in adaptive analysis with the smaller number of elements as compared to mesh dependent RPI and mesh dependent least square. It is also concluded that proposed mesh free recovery technique may prove to be most suitable for error recovery and adaptive analysis of problems dealing with large domain changes and domain discontinuities.

Keywords: error estimation; effectivity; basis function; meshfree recovery technique; radial point interpolation; radial basis function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/16/1900/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/16/1900/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:16:p:1900-:d:611490

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().