Meshless Methods in Biomechanics

Bone Tissue Remodelling Analysis
2014
ISBN: 978-3-319-06399-7
Verlag: Springer International Publishing

Buch, Englisch, Band 16, 320 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 6269 g

Reihe: Lecture Notes in Computational Vision and Biomechanics

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.

Zielgruppe

Research

Autoren/Hrsg.

Belinha, Jorge

Fachgebiete

• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computersimulation & Modelle, 3-D Graphik
• Technische Wissenschaften Technik Allgemein Modellierung & Simulation
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Medizintechnik, Biomedizintechnik
• Medizin | Veterinärmedizin Medizin | Public Health | Pharmazie | Zahnmedizin Medizin, Gesundheitswesen Medizintechnik, Biomedizintechnik, Medizinische Werkstoffe
• Naturwissenschaften Physik Angewandte Physik Biophysik

Inhaltsverzeichnis

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.