A traction-based equilibrium finite element free from spurious kinematic modes for linear elasticity problems

2014 ◽  
Vol 99 (10) ◽  
pp. 763-788 ◽  
Author(s):  
Li Wang ◽  
Hongzhi Zhong
Keyword(s):  
Finite Element ◽  
Linear Elasticity ◽  
Elasticity Problems ◽  
Element Free

scholarly journals Element Free Galerkin Post-processing Technique Based Error Estimator for Elasticity Problems

2018 ◽  
Vol 4 (12) ◽  
pp. 2946 ◽  
Author(s):  
Mohd. Ahmed ◽  
Devender Singh ◽  
M. Noor Desmukh
Keyword(s):  
Finite Element ◽  
Processing Technique ◽  
Error Estimator ◽  
Post Processing ◽  
Element Analysis ◽  
Quadrilateral Elements ◽  
Mesh Free ◽  
Elasticity Problems ◽  
Analysis Application ◽  
Element Free

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.

A reduced basis approach for rapid and reliable computation of structural linear elasticity problems using mixed interpolation of tensorial components element

2012 ◽  
Vol 227 (5) ◽  
pp. 905-918 ◽  
Author(s):  
F Lei ◽  
YL Ma ◽  
YC Bai ◽  
HB Yang
Keyword(s):  
Finite Element ◽  
Linear Elasticity ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Lower Dimension ◽  
Adaptive Procedure ◽  
Reduced Basis ◽  
Structural Problem ◽  
Elasticity Problems ◽  
Basis Method

As the reduced basis method is well used in some other fields to rapidly solve engineer systems, it is adapted to structural computation here. In this article, a reduced basis approach of computing structural linear elasticity problems is proposed to obtain rapid and reliable outputs using mixed interpolation of tensorial components elements. The procedure is as follows. First, structural computation problems based on finite element formulation should be parametrized. As an example, finite element formulation based on a type of element is analyzed and parameters in the formulation are extracted explicitly. Parametrized structural problem is built by assembling finite element formulation of components with parameters. Then, an approximate subspace of lower dimension based on structural outputs within whole parameter domain is constructed by an adaptive procedure. By projecting the parametrized structural problem onto that subspace, it is reduced to a parametrized lower dimension problem, which can be solved rapidly with random given parameters. The procedure is divided into two phases, naming offline and online procedure. Structures in vehicle design problems are employed to verify the feasibility of the procedure and deviation of the accuracy. The results showed that reduced basis approach of structural computation is applicable and efficient.

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