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Meshless Methods in Biomechanics [electronic resource] : Bone Tissue Remodelling Analysis / by Jorge Belinha.

By: Belinha, Jorge [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Lecture Notes in Computational Vision and Biomechanics: 16Publisher: Cham : Springer International Publishing : Imprint: Springer, 2014Description: XIII, 320 p. 208 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319064000.Subject(s): Engineering | Computer mathematics | Numerical analysis | Structural mechanics | Mechanical engineering | Biomedical engineering | Engineering | Biomedical Engineering | Structural Mechanics | Numerical Analysis | Computational Science and Engineering | Mechanical EngineeringAdditional physical formats: Printed edition:: No titleDDC classification: 610.28 Online resources: Click here to access online
Contents:
1. Introduction -- 1.1 Meshless Methods -- 1.2 Natural Neighbour Radial Point Interpolation Method -- 1.3 Bone tissue remodelling analysis -- 1.4 Book Purpose -- 1.5 Meshless method software -- 1.6 Book arrangement -- 2. Solid Mechanics Fundamentals -- 2.1 Continuum formulation -- 2.2 Weak form -- 2.3 Discrete system of equations -- 3. Meshless Methods Introduction -- 3.1 Meshless generic procedure -- 3.2 Nodal connectivity -- 3.3 Numerical integration -- 3.4 Numerical implementation -- 4. Shape Functions -- 4.1 Introduction -- 4.2 Support-Domain -- 4.3 Moving Least Squares -- 4.4 Radial Point Interpolators -- 5. Solid Mechanics Problems -- 5.1 Solid Mechanics NNRPIM flow chart -- 5.2 RPI shape function patch test -- 5.3 Elastostatic numerical examples -- 5.4 Elastodynamic numerical examples -- 6. Bone Tissue -- 6.1 Bone biology: Basic concepts -- 6.2 Bone tissue mechanical properties -- 6.3 Bone remodelling algorithms -- 7. Bone Tissue Remodelling Analysis -- 7.1 Bone Patch Analysis -- 7.2 Bone Structures -- 7.3 Implants -- 8. References -- 9. Subject Index.
In: Springer eBooksSummary: This book presents the complete formulation of a new advanced discretization meshless technique: the Natural Neighbour Radial Point Interpolation Method (NNRPIM). In addition, two of the most popular meshless methods, the EFGM and the RPIM, are fully presented. Being a truly meshless method, the major advantages of the NNRPIM over the FEM, and other meshless methods, are the remeshing flexibility and the higher accuracy of the obtained variable field. Using the natural neighbour concept, the NNRPIM permits to determine organically the influence-domain, resembling the cellulae natural behaviour. This innovation permits the analysis of convex boundaries and extremely irregular meshes, which is an advantage in the biomechanical analysis, with no extra computational effort associated.   This volume shows how to extend the NNRPIM to the bone tissue remodelling analysis, expecting to contribute with new numerical tools and strategies in order to permit a more efficient numerical biomechanical analysis.
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1. Introduction -- 1.1 Meshless Methods -- 1.2 Natural Neighbour Radial Point Interpolation Method -- 1.3 Bone tissue remodelling analysis -- 1.4 Book Purpose -- 1.5 Meshless method software -- 1.6 Book arrangement -- 2. Solid Mechanics Fundamentals -- 2.1 Continuum formulation -- 2.2 Weak form -- 2.3 Discrete system of equations -- 3. Meshless Methods Introduction -- 3.1 Meshless generic procedure -- 3.2 Nodal connectivity -- 3.3 Numerical integration -- 3.4 Numerical implementation -- 4. Shape Functions -- 4.1 Introduction -- 4.2 Support-Domain -- 4.3 Moving Least Squares -- 4.4 Radial Point Interpolators -- 5. Solid Mechanics Problems -- 5.1 Solid Mechanics NNRPIM flow chart -- 5.2 RPI shape function patch test -- 5.3 Elastostatic numerical examples -- 5.4 Elastodynamic numerical examples -- 6. Bone Tissue -- 6.1 Bone biology: Basic concepts -- 6.2 Bone tissue mechanical properties -- 6.3 Bone remodelling algorithms -- 7. Bone Tissue Remodelling Analysis -- 7.1 Bone Patch Analysis -- 7.2 Bone Structures -- 7.3 Implants -- 8. References -- 9. Subject Index.

This book presents the complete formulation of a new advanced discretization meshless technique: the Natural Neighbour Radial Point Interpolation Method (NNRPIM). In addition, two of the most popular meshless methods, the EFGM and the RPIM, are fully presented. Being a truly meshless method, the major advantages of the NNRPIM over the FEM, and other meshless methods, are the remeshing flexibility and the higher accuracy of the obtained variable field. Using the natural neighbour concept, the NNRPIM permits to determine organically the influence-domain, resembling the cellulae natural behaviour. This innovation permits the analysis of convex boundaries and extremely irregular meshes, which is an advantage in the biomechanical analysis, with no extra computational effort associated.   This volume shows how to extend the NNRPIM to the bone tissue remodelling analysis, expecting to contribute with new numerical tools and strategies in order to permit a more efficient numerical biomechanical analysis.

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