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

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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).

    Original languageEnglish
    Pages (from-to)902-920
    Number of pages19
    JournalEngineering Computations (Swansea, Wales)
    Volume34
    Issue number3
    DOIs
    Publication statusPublished - Apr 2017

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    Galerkin methods
    Elasticity
    Mechanics
    Boundary value problems
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    Cite this

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    title = "Computation of accurate solutions when using element-free Galerkin methods for solving structural problems",
    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 = "Adaptive quadrature, Dynamic relaxation, Element-free Galerkin methods, Explicit integration, Total Lagrangian formulation",
    author = "Joldes, {Grand Roman} and Peter Teakle and Adam Wittek and Karol Miller",
    year = "2017",
    month = "4",
    doi = "10.1108/EC-01-2016-0017",
    language = "English",
    volume = "34",
    pages = "902--920",
    journal = "Engineering Computations (Swansea, Wales)",
    issn = "0264-4401",
    publisher = "Emerald Group Publishing Limited",
    number = "3",

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    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

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    U2 - 10.1108/EC-01-2016-0017

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