An element free Galerkin Method for the prediction of soft tissue deformation in surgical simulation

Habibullah Amin Chowdhury

    Research output: ThesisDoctoral Thesis

    Abstract

    Meshless methods based on Element Free Galerkin formulation exhibit three major limitations : a) meshless shape functions using higher order basis cannot always be computed for arbitrarily distributed nodes; b) challenges in imposing the Essential Boundary Conditions (EBC), and, c) inaccurate numerical integration in space. To find effective solutions for the problems mentioned, the thesis presents a Modified Moving Least Squares method for interpolating scattered data, a novel way of imposing EBC for explicit meshless, and implements an adaptive numerical integration procedure. The effectiveness of the proposed methods is demonstrated using 2D and 3D numerical examples of soft tissue deformation.
    LanguageEnglish
    QualificationDoctor of Philosophy
    Awarding Institution
    • The University of Western Australia
    Thesis sponsors
    Award date3 Nov 2017
    DOIs
    StatePublished - 2017

    Fingerprint

    Galerkin methods
    Boundary conditions
    Tissue

    Cite this

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    title = "An element free Galerkin Method for the prediction of soft tissue deformation in surgical simulation",
    abstract = "Meshless methods based on Element Free Galerkin formulation exhibit three major limitations : a) meshless shape functions using higher order basis cannot always be computed for arbitrarily distributed nodes; b) challenges in imposing the Essential Boundary Conditions (EBC), and, c) inaccurate numerical integration in space. To find effective solutions for the problems mentioned, the thesis presents a Modified Moving Least Squares method for interpolating scattered data, a novel way of imposing EBC for explicit meshless, and implements an adaptive numerical integration procedure. The effectiveness of the proposed methods is demonstrated using 2D and 3D numerical examples of soft tissue deformation.",
    keywords = "Meshless method, Element free Galerkin, Soft tissue deformation, Essential boundary condition, Numerical integration, Modified moving least squares",
    author = "Chowdhury, {Habibullah Amin}",
    year = "2017",
    doi = "10.4225/23/5a1273d4df3ff",
    language = "English",
    school = "The University of Western Australia",

    }

    Chowdhury, HA 2017, 'An element free Galerkin Method for the prediction of soft tissue deformation in surgical simulation', Doctor of Philosophy, The University of Western Australia. DOI: 10.4225/23/5a1273d4df3ff

    An element free Galerkin Method for the prediction of soft tissue deformation in surgical simulation. / Chowdhury, Habibullah Amin.

    2017.

    Research output: ThesisDoctoral Thesis

    TY - THES

    T1 - An element free Galerkin Method for the prediction of soft tissue deformation in surgical simulation

    AU - Chowdhury,Habibullah Amin

    PY - 2017

    Y1 - 2017

    N2 - Meshless methods based on Element Free Galerkin formulation exhibit three major limitations : a) meshless shape functions using higher order basis cannot always be computed for arbitrarily distributed nodes; b) challenges in imposing the Essential Boundary Conditions (EBC), and, c) inaccurate numerical integration in space. To find effective solutions for the problems mentioned, the thesis presents a Modified Moving Least Squares method for interpolating scattered data, a novel way of imposing EBC for explicit meshless, and implements an adaptive numerical integration procedure. The effectiveness of the proposed methods is demonstrated using 2D and 3D numerical examples of soft tissue deformation.

    AB - Meshless methods based on Element Free Galerkin formulation exhibit three major limitations : a) meshless shape functions using higher order basis cannot always be computed for arbitrarily distributed nodes; b) challenges in imposing the Essential Boundary Conditions (EBC), and, c) inaccurate numerical integration in space. To find effective solutions for the problems mentioned, the thesis presents a Modified Moving Least Squares method for interpolating scattered data, a novel way of imposing EBC for explicit meshless, and implements an adaptive numerical integration procedure. The effectiveness of the proposed methods is demonstrated using 2D and 3D numerical examples of soft tissue deformation.

    KW - Meshless method

    KW - Element free Galerkin

    KW - Soft tissue deformation

    KW - Essential boundary condition

    KW - Numerical integration

    KW - Modified moving least squares

    U2 - 10.4225/23/5a1273d4df3ff

    DO - 10.4225/23/5a1273d4df3ff

    M3 - Doctoral Thesis

    ER -