CONTENTS -- BIOGRAPHICAL INFORMATION -- Preface -- 1. COMPUTATIONAL MODELLING -- 1.1 INTRODUCTION -- 1.2 PHYSICAL PROBLEMS IN ENGINEERING -- 1.3 COMPUTATIONAL MODELLING USING THE FEM -- 1.3.1 Modelling of the Geometry -- 1.3.2 Meshing -- 1.3.3 Property of Material or Medium -- 1.3.4 Boundary, Initial and Loading Conditions -- 1.4 SIMULATION -- 1.4.1 Discrete System Equations -- 1.4.2 Equation Solvers -- 1.5 VISUALIZATION -- 2. INTRODUCTION TO MECHANICS FOR SOLIDS AND STRUCTURES -- 2.1 INTRODUCTION -- 2.2 EQUATIONS FOR THREE-DIMENSIONAL SOLIDS -- 2.2.1 Stress and Strain -- 2.2.2 Constitutive Equations -- 2.2.3 Dynamic Equilibrium Equation -- 2.2.4 Boundary Conditions -- 2.3 EQUATIONS FOR TWO-DIMENSIONAL SOLIDS -- 2.3.1 Stress and Strain -- 2.3.2 Constitutive Equations -- 2.3.3 Dynamic Equilibrium Equations -- 2.4 EQUATIONS FOR TRUSS MEMBERS -- 2.4.1 Stress and Strain -- 2.4.2 Constitutive Equations -- 2.4.3 Dynamic Equilibrium Equations -- 2.5 EQUATIONS FOR BEAMS -- 2.5.1 Stress and Strain -- 2.5.2 Constitutive Equations -- 2.5.3 Moments and Shear Forces -- 2.5.4 Dynamic Equilibrium Equations -- 2.6 EQUATIONS FOR PLATES -- 2.6.1 Stress and Strain -- 2.6.2 Constitutive Equations -- 2.6.3 Moments and Shear Forces -- 2.6.4 Dynamic Equilibrium Equations -- 2.6.5 Reissner-Mindlin Plate (Reissner, 1945 -- Mindlin, 1951) -- 2.7 REMARKS -- 3. FUNDAMENTALS FOR FINITE ELEMENT METHOD -- 3.1 INTRODUCTION -- 3.2 STRONG AND WEAK FORMS -- 3.3 HAMILTON'S PRINCIPLE -- 3.4 FEM PROCEDURE -- 3.4.1 Domain Discretization -- 3.4.2 Displacement Interpolation -- 3.4.3 Standard Procedure for Constructing Shape Functions -- 3.4.4 Properties of the Shape Functions1 -- 3.4.5 Formation of FE Equations in Local Coordinate System -- 3.4.6 Coordinate transformation -- 3.4.7 Assembly of Global FE Equation -- 3.4.8 Imposition of Displacement Constraints.

3.4.9 Solving the Global FE Equation -- 3.5 STATIC ANALYSIS -- 3.6 ANALYSIS OF FREE VIBRATION (EIGENVALUE ANALYSIS) -- 3.7 TRANSIENT RESPONSE -- 3.7.1 Central Difference Algorithm -- 3.7.2 Newmark's Method (Newmark, 1959) -- 3.8 REMARKS -- 3.8.1 Summary of Shape Function Properties -- 3.8.2 Sufficient Requirements for FEM Shape Functions -- 3.8.3 Recap of FEM Procedure -- 3.9 REVIEW QUESTIONS -- 4. FEM FOR TRUSSES -- 4.1 INTRODUCTION -- 4.2 FEM EQUATIONS -- 4.2.1 Shape Function Construction -- 4.2.2 Strain Matrix -- 4.2.3 Element Matrices in the Local Coordinate System -- 4.2.4 Element Matrices in the Global Coordinate System -- 4.2.5 Boundary Conditions -- 4.2.6 Recovering Stress and Strain -- 4.3 WORKED EXAMPLES -- Example 4.1: A uniform bar subjected to an axial force -- 4.3.1 Properties of the FEM -- Example 4.2: A triangular truss structure subjected to a vertical force -- 4.4 HIGH ORDER ONE-DIMENSIONAL ELEMENTS -- 4.5 REVIEW QUESTIONS -- 5. FEM FOR BEAMS -- 5.1 INTRODUCTION -- 5.2 FEM EQUATIONS -- 5.2.1 Shape Function Construction -- 5.2.2 Strain Matrix -- 5.2.3 Element Matrices -- 5.3 REMARKS -- 5.4 WORKED EXAMPLES -- Example 5.1: A uniform cantilever beam subjected to a downward force -- 5.5 CASE STUDY: RESONANT FREQUENCIES OF MICRO RESONANT TRANSDUCER -- 5.5.1 Modelling -- 5.5.2 ABAQUS Input File -- 5.5.3 Solution Process -- 5.5.4 Result and Discussion -- 5.6 REVIEW QUESTIONS -- 6. FEM FOR FRAMES -- 6.1 INTRODUCTION -- 6.2 FEM EQUATIONS FOR PLANAR FRAMES -- 6.2.1 Equations in Local Coordinate System -- 6.2.2 Equations in Global Coordinate System -- 6.3 FEM EQUATIONS FOR SPACE FRAMES -- 6.3.1 Equations in Local Coordinate System -- 6.3.2 Equations in Global Coordinate System -- 6.4 REMARKS -- 6.5 CASE STUDY: FINITE ELEMENT ANALYSIS OF A BICYCLE FRAME -- 6.5.1 Modelling -- 6.5.2 Abaqus Input File -- 6.5.3 Solution Processes.

6.5.4 Results and Discussion -- 6.6 REVIEW QUESTIONS -- 7. FEM FOR TWO-DIMENSIONAL SOLIDS -- 7.1 INTRODUCTION -- 7.2 LINEAR TRIANGULAR ELEMENTS -- 7.2.1 Field Variable Interpolation -- 7.2.2 Shape Function Construction -- 7.2.3 Area Coordinates -- 7.2.4 Strain Matrix -- 7.2.5 Element Matrices -- 7.3 LINEAR RECTANGULAR ELEMENTS -- 7.3.1 Shape Function Construction -- 7.3.2 Strain Matrix -- 7.3.3 Element Matrices -- 7.3.4 Gauss Integration -- 7.4 LINEAR QUADRILATERAL ELEMENTS -- 7.4.1 Coordinate Mapping -- 7.4.2 Strain Matrix -- 7.4.3 Element Matrices -- 7.4.4 Remarks -- 7.5 HIGHER ORDER ELEMENTS -- 7.5.1 Triangular Element Family -- 7.5.2 Rectangular Elements -- 7.6 ELEMENTS WITH CURVED EDGES -- 7.7 COMMENTS ON GAUSS INTEGRATION -- 7.8 CASE STUDY: SIDE DRIVE MICRO-MOTOR -- 7.8.1 Modelling -- 7.8.2 ABAQUS Input File -- 7.8.3 Solution Process -- 7.8.4 Results and Discussion -- 7.9 REVIEW QUESTIONS (PETYT, 1990) -- 8. FEM FOR PLATES AND SHELLS -- 8.1 INTRODUCTION -- 8.2 PLATE ELEMENTS -- 8.2.1 Shape Functions -- 8.2.2 Element Matrices -- 8.2.3 Higher Order Elements -- 8.3 SHELL ELEMENTS -- 8.3.1 Elements in Local Coordinate Systems -- 8.3.2 Elements in Global Coordinate System -- 8.4 REMARKS -- 8.5 CASE STUDY: NATURAL FREQUENCIES OF MICRO-MOTOR -- 8.5.1 Modelling -- 8.5.2 ABAQUS Input File -- 8.5.3 Solution Process -- 8.5.4 Result and Discussion -- 8.6 CASE STUDY: TRANSIENT ANALYSIS OF A MICRO-MOTOR -- 8.6.1 Modelling -- 8.6.2 ABAQUS Input File -- 8.6.3 Solution Process -- 8.6.4 Result and Discussion -- 8.7 REVIEW QUESTIONS -- 9. FEM FOR 3D SOLIDS -- 9.1 INTRODUCTION -- 9.2 TETRAHEDRON ELEMENT -- 9.2.1 Strain Matrix -- 9.2.2 Element Matrices -- 9.3 HEXAHEDRON ELEMENT -- 9.3.1 Strain Matrix -- 9.3.2 Element Matrices -- 9.3.3 Using Tetrahedrons to form Hexahedrons -- 9.4 HIGHER ORDER ELEMENTS -- 9.4.1 Tetrahedron Elements -- 9.4.2 Brick Elements.

9.5 ELEMENTS WITH CURVED SURFACES -- 9.6 CASE STUDY: STRESS AND STRAIN ANALYSIS OF A QUANTUM DOT HETEROSTRUCTURE -- 9.6.1 Modelling -- 9.6.2 ABAQUS Input File -- 9.6.3 Solution Process -- 9.6.4 Result and Discussion -- 9.7 REVIEW QUESTIONS -- 10. SPECIAL PURPOSE ELEMENTS -- 10.1 INTRODUCTION -- 10.2 CRACK TIP ELEMENTS -- 10.3 METHODS FOR INFINITE DOMAINS -- 10.3.1 Infinite Element Formulated by Mapping (Bettess, 1992) -- 10.3.2 Gradual Damping Elements -- 10.3.3 Coupling of FEM and BEM -- 10.3.4 Coupling of FEM and SEM -- 10.4 FINITE STRIP ELEMENTS -- 10.5 STRIP ELEMENT METHOD (SEM) -- 11. MODELLING TECHNIQUES -- 11.1 INTRODUCTION -- 11.2 CPU TIME ESTIMATION -- 11.3 GEOMETRY MODELLING -- 11.4 MESHING -- 11.4.1 Mesh Density -- 11.4.2 Element Distortion -- 11.5 MESH COMPATIBILITY -- 11.5.1 Different Order of Elements -- 11.5.2 Straddling Elements -- 11.6 USE OF SYMMETRY -- 11.6.1 Mirror Symmetry or Plane Symmetry -- 11.6.2 Axial Symmetry -- 11.6.3 Cyclic Symmetry -- 11.6.4 Repetitive Symmetry -- 11.7 MODELLING OF OFFSETS -- 11.7.1 Methods for Modelling Offsets -- 11.7.2 Creation of MPC Equations for Offsets -- 11.8 MODELLING OF SUPPORTS -- 11.9 MODELLING OF JOINTS -- 11.10 OTHER APPLICATIONS OF MPC EQUATIONS -- 11.10.1 Modelling of Symmetric Boundary Conditions -- 11.10.2 Enforcement of Mesh Compatibility -- 11.10.3 Modelling of Constraints by Rigid Body Attachment -- 11.11 IMPLEMENTATION OF MPC EQUATIONS -- 11.11.1 Lagrange Multiplier Method -- 11.11.2 Penalty Method -- 11.12 REVIEW QUESTIONS -- 12. FEM FOR HEAT TRANSFER PROBLEMS -- 12.1 FIELD PROBLEMS -- 12.1.1 Heat Transfer in a Two-Dimensional Fin -- 12.1.2 Heat Transfer in a Long Two-Dimensional Body -- 12.1.3 Heat Transfer in a One-Dimensional Fin -- 12.1.4 Heat Transfer Across a CompositeWall -- 12.1.5 Torsional Deformation of a Bar -- 12.1.6 Ideal Irrotational Fluid Flow.

12.1.7 Acoustic Problems -- 12.2 WEIGHTED RESIDUAL APPROACH FOR FEM -- 12.3 1D HEAT TRANSFER PROBLEM -- 12.3.1 One-Dimensional Fin -- 12.3.2 Direct Assembly Procedure -- 12.3.3 Worked Example -- 12.3.4 Remarks -- 12.3.5 CompositeWall -- 12.3.6 Worked Example -- 12.4 2D HEAT TRANSFER PROBLEM -- 12.4.1 Element Equations -- 12.4.2 Triangular Elements -- 12.4.3 Rectangular Elements -- 12.4.4 Boundary Conditions and Vector b( -- 12.4.5 Point Heat Source or Sink -- 12.5 SUMMARY -- 12.6 CASE STUDY: TEMPERATURE DISTRIBUTION OF HEATED ROAD SURFACE -- 12.6.1 Modelling -- 12.6.2 ABAQUS Input File -- 12.6.3 Result and Discussion -- 12.7 REVIEW QUESTIONS -- 13. USING ABAQUS -- 13.1 INTRODUCTION -- 13.2 BASIC BUILDING BLOCK: KEYWORDS AND DATA LINES -- 13.3 USING SETS -- 13.4 ABAQUS INPUT SYNTAX RULES -- 13.4.1 Keyword Lines -- 13.4.2 Data Lines -- 13.4.3 Labels -- 13.5 DEFINING A FINITE ELEMENT MODEL IN ABAQUS -- 13.5.1 Model Data -- 13.5.2 History Data -- 13.5.3 Example of Cantilever Beam Problem -- 13.6 GENERAL PROCEDURES -- REFERENCES -- INDEX.