Abstract
The study present a Mesh Free based post-processing technique for asymptotically (upper) bounded error estimator for Finite Element Analyses of elastic problems. The proposed technique uses Galerkin Element Free procedure for recovery of the displacement derivatives over a patch of nodes in radial domains. The radial nodes patches are used to construct the trial shape functions utilizing the moving least-squares (MLS) techniques. The proposed technique has been tested on three benchmark elastic problems discretized using 4-node quadrilateral elements. The recovered nodal stresses are utilized to calculate the error in finite element solution in energy norm. The study also demonstrates adaptive analysis application of proposed error estimator. The performance of proposed error estimator based on mesh independent node patches has been compared with that of mesh dependent node patches based Zienkiewicz-Zhu (ZZ) error estimator on structured and unstructured mesh. The improved results of the proposed error estimator in terms of convergence rate and effectivity are obtained. It is shown that present study incorporates the superiority of the Mesh Free Galerkin method into finite element analysis environment.
Highlights
With advent of powerful computer system, finite element method has gained considerable prominence in industry
The background meshing scheme and their node locations used by the Element Free Galerkin (EFG) as well as Zienkiewicz- Zhu (ZZ) post processing procedure are the same
It is evident from the analysis results that the error convergence obtained with the help of proposed element free Galerkin (EFG) error estimator is found to be superior to that for the ZZ super convergent recovery procedure based error estimator considering various mesh schemes
Summary
With advent of powerful computer system, finite element method has gained considerable prominence in industry. Errors are introduced into the finite element method by the very process of subdividing the problem into sub regions. Much attention has been paid to develop error estimators to quantify the Finite Element solution errors. A state-of-art of different error estimation technique developed to get the practical finite solution of linear, non-linear and transient problems analyses are presented by Gratsch and Bathe [4]. Nadal et al [5] proposes the explicit-type recovery error estimator in energy norm for the linear elasticity problem using smooth solution. Hannukainen et al [6] have developed a posteriori error estimate and showed improved convergence in non-coinciding meshes for problems of linear elasticity. Riedlbeck et al [8] have presented a posteriori error estimate based on an
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