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Basic finite element method as applied to injury biomechanics
Front Cover; Basic Finite Element Method as Applied to Injury Biomechanics; Basic Finite Element Method as Applied toInjury Biomechanics; Copyright; Contents; List of Contributors; Foreword; Preface; 1 -- Basic Finite ElementMethod and Analysisas Applied to Injury Biomechanics; 1 -- Introduction; 1.1 FINITE ELEMENT METHOD AND ANALYSIS; 1.2 CALCULATION OF STRAIN AND STRESS FROM THE FE MODEL; 1.2.1 AVERAGE STRAIN AND POINT STRAIN; 1.2.2 NORMAL AND SHEAR STRAIN; 1.2.3 CALCULATION OF STRESS; 1.3 SAMPLE MATRIX STRUCTURAL ANALYSIS; 1.3.1 ELEMENT STIFFNESS MATRIX OF A LINEAR SPRING.
1.3.2 ELEMENT STIFFNESS MATRIX OF A LINEAR SPRING NOT IN LINE WITH THE X-AXIS1.3.3 ELEMENT STIFFNESS MATRIX OF A HOMOGENEOUS LINEAR ELASTIC BAR; 1.3.4 GLOBAL STIFFNESS MATRIX OF MULTIPLE INLINE LINEAR SPRINGS OR BARS; 1.3.5 GLOBAL STIFFNESS MATRIX OF A SIMPLE BIOMECHANICS PROBLEM; 1.3.6 GLOBAL STIFFNESS MATRIX OF A SIMPLE TRUSS BRIDGE; 1.3.7 GAUSSIAN OR GAUSS ELIMINATION; 1.4 FROM MSA TO A FINITE ELEMENT MODEL; REFERENCES; 2 -- Meshing, Element Types, and Element Shape Functions; 2.1 STRUCTURE IDEALIZATION AND DISCRETIZATION; 2.2 NODE; 2.3 ELEMENT; 2.3.1 SIMPLEST ELEMENT TYPES.
2.3.2 1D ELEMENT TYPE2.3.3 2D ELEMENT TYPE; 2.3.4 3D ELEMENT TYPE; 2.4 FORMATION OF FINITE ELEMENT MESH; 2.5 ELEMENT SHAPE FUNCTIONS AND [B] MATRIX; 2.5.1 1D, 2-NODE ELEMENT SHAPE FUNCTIONS; 2.5.1.1 2-Node Linear Bar Element; 2.5.1.2 2-Node Beam Element; 2.5.2 2D, 3-NODE LINEAR TRIANGULAR ELEMENT; 2.5.2.1 3-Node Linear Triangular Element; 2.5.3 4-NODE RECTANGULAR BILINEAR PLANE ELEMENT WITH EDGES PARALLEL TO THE COORDINATE AXES; 2.5.3.1 Comparison of CST and Bilinear Quadrilateral Element; 2.5.4 2D, 4-NODE PLATE ELEMENT SHAPE FUNCTIONS WITH EDGES PARALLEL TO THE COORDINATE AXES.
2.5.4.1 Use Pascal's Triangle to Select Polynomial Terms2.5.4.2 Select Polynomial Functions to Interpolate a Four-Node Plate Element; 2.5.4.3 Identify 12 Constants for the Interpolation Polynomial; 2.5.4.4 Find Shape Functions for a 4-Node Plate Element; 2.5.4.5 Determine Strain-Displacement Matrix; 2.5.5 3D, 4-NODE SHELL ELEMENT; 2.5.6 3D, 8-NODE TRILINEAR ELEMENT SHAPE FUNCTIONS; REFERENCES; 3 -- Isoparametric Formulation and Mesh Quality; 3.1 INTRODUCTION; 3.2 NATURAL COORDINATE SYSTEM; 3.3 ISOPARAMETRIC FORMULATION OF 1D ELEMENTS; 3.3.1 1D LINEAR BAR ELEMENT ISOPARAMETRIC SHAPE FUNCTIONS.
3.3.1.1 1D Transfer Mapping Functions and Interpolations3.3.2 1D BEAM ELEMENT ISOPARAMETRIC SHAPE FUNCTIONS; 3.4 ISOPARAMETRIC FORMULATION OF 2D ELEMENT; 3.4.1 ISOPARAMETRIC FORMULATION OF 2D TRIANGULAR ELEMENT; 3.4.2 ISOPARAMETRIC FORMULATION OF 2D BILINEAR ELEMENT; 3.4.3 DETERMINE THE [B] MATRIX BASED ON ISOPARAMETRIC FORMULATION; 3.5 ISOPARAMETRIC FORMULATION OF 3D ELEMENT; 3.5.1 CONSTANT-STRAIN TETRAHEDRAL ELEMENT; 3.5.2 TRILINEAR HEXAHEDRAL ELEMENT; 3.6 TRANSFER MAPPING FUNCTION FOR 2D ELEMENT; 3.7 JACOBIAN MATRIX AND DETERMINANT OF JACOBIAN MATRIX.
1. Introduction 2. Meshing, Element Types, and Element Shape Functions 3. Isoparametric Formulation and Mesh Quality 4. Element Stiffness Matrix 5. Material Laws and Properties 6. Boundary and loading conditions 7. Stepping through finite element analysis 8. Modal and Transient Dynamic Solutions 9. Biological Components Modeling 10. Parametric Modeling 11. Modeling passive and active muscle 12. Modeling the Head 13. Modeling the Neck 14. Modeling the Upper Torso and Upper Extremity 15. Modeling the Lower Torso 16. Modeling the Lower Extremity 17. Modeling Vulnerable subjects 18. Fundamentals of Blast Modeling.