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Computation of accurate solutions when using element-free Galerkin methods for solving structural problems

Grand Roman Joldes (Intelligent Systems for Medicine Laboratory, School of Mechanical and Chemical Engineering, The University of Western Australia , Perth, Australia)
Peter Teakle (Intelligent Systems for Medicine Laboratory, School of Mechanical and Chemical Engineering, The University of Western Australia , Perth, Australia)
Adam Wittek (Intelligent Systems for Medicine Laboratory, School of Mechanical and Chemical Engineering, The University of Western Australia , Perth, Australia)
Karol Miller (Intelligent Systems for Medicine Laboratory, School of Mechanical and Chemical Engineering, The University of Western Australia , Perth, Australia)

Engineering Computations

ISSN: 0264-4401

Article publication date: 2 May 2017

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Abstract

Purpose

This paper aims to investigate the application of adaptive integration in element-free Galerkin methods for solving problems in structural and solid mechanics to obtain accurate reference solutions.

Design/methodology/approach

An adaptive quadrature algorithm which allows user control over integration accuracy, previously developed for integrating boundary value problems, is adapted to elasticity problems. The algorithm allows the development of a convergence study procedure that takes into account both integration and discretisation errors. The convergence procedure is demonstrated using an elasticity problem which has an analytical solution and is then applied to accurately solve a soft-tissue extension problem involving large deformations.

Findings

The developed convergence procedure, based on the presented adaptive integration scheme, allows the computation of accurate reference solutions for challenging problems which do not have an analytical or finite element solution.

Originality/value

This paper investigates the application of adaptive quadrature to solid mechanics problems in engineering analysis using the element-free Galerkin method to obtain accurate reference solutions. The proposed convergence procedure allows the user to independently examine and control the contribution of integration and discretisation errors to the overall solution error. This allows the computation of reference solutions for very challenging problems which do not have an analytical or even a finite element solution (such as very large deformation problems).

Keywords

Acknowledgements

This research was supported partially by the Australian Government through the Australian Research Council's Discovery Projects funding scheme (projects DP1092893, DP120100402 and DP160100714). The views expressed herein are those of the authors and are not necessarily those of the Australian Government or Australian Research Council. The authors wish to acknowledge the Raine Medical Research Foundation for funding G.R. Joldes through a Raine Priming Grant.

Citation

Joldes, G.R., Teakle, P., Wittek, A. and Miller, K. (2017), "Computation of accurate solutions when using element-free Galerkin methods for solving structural problems", Engineering Computations, Vol. 34 No. 3, pp. 902-920. https://doi.org/10.1108/EC-01-2016-0017

Publisher

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Emerald Publishing Limited Bingley, United Kingdom

Copyright © 2017, Emerald Publishing Limited