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).
| Original language | English |
|---|---|
| Pages (from-to) | 902-920 |
| Number of pages | 19 |
| Journal | Engineering Computations (Swansea, Wales) |
| Volume | 34 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Apr 2017 |
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Computation of accurate solutions when using element-free Galerkin methods for solving structural problems. / Joldes, Grand Roman; Teakle, Peter; Wittek, Adam; Miller, Karol.
In: Engineering Computations (Swansea, Wales), Vol. 34, No. 3, 04.2017, p. 902-920.Research output: Contribution to journal › Article
TY - JOUR
T1 - Computation of accurate solutions when using element-free Galerkin methods for solving structural problems
AU - Joldes, Grand Roman
AU - Teakle, Peter
AU - Wittek, Adam
AU - Miller, Karol
PY - 2017/4
Y1 - 2017/4
N2 - 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).
AB - 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).
KW - Adaptive quadrature
KW - Dynamic relaxation
KW - Element-free Galerkin methods
KW - Explicit integration
KW - Total Lagrangian formulation
UR - http://www.scopus.com/inward/record.url?scp=85020738875&partnerID=8YFLogxK
U2 - 10.1108/EC-01-2016-0017
DO - 10.1108/EC-01-2016-0017
M3 - Article
VL - 34
SP - 902
EP - 920
JO - Engineering Computations (Swansea, Wales)
JF - Engineering Computations (Swansea, Wales)
SN - 0264-4401
IS - 3
ER -