Half Title -- Title Page -- Copyright -- Dedication -- Biography -- Contents -- Preface to the First Edition -- 1 Computational Modeling -- 1.1 Introduction -- 1.2 Physical problems in engineering -- 1.3 Computational modeling using FEM -- 1.3.1 Modeling of the geometry -- 1.3.2 Meshing -- 1.3.3 Material or medium properties -- 1.3.4 Boundary, initial, and loading conditions -- 1.4 Solution procedure -- 1.4.1 Discrete system equations -- 1.4.2 Equation solvers -- 1.5 Results visualization -- 2 Briefing on 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 equations -- 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 -- Solution -- 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 -- 2.7 Remarks -- 2.8 Review questions -- 3 Fundamentals for Finite Element Method -- 3.1 Introduction -- 3.2 Strong and weak forms: problem formulation -- 3.3 Hamilton's principle: A weak formulation -- 3.3.1 Hamilton's principle -- 3.3.2 Minimum total potential energy principle -- 3.4 FEM procedure -- 3.4.1 Domain discretization -- 3.4.2 Displacement interpolation -- 3.4.3 Standard procedure for constructing shape functions -- 3.4.3.1 On the inverse of the moment matrix.

3.4.3.2 On the compatibility of the shape functions -- 3.4.3.3 On other means of construct shape functions -- 3.4.4 Properties of the shape functions -- 3.4.5 Formulation of finite element 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 -- 4.2.4.1 Spatial trusses -- 4.2.4.2 Planar trusses -- 4.2.5 Boundary conditions -- 4.2.6 Recovering stress and strain -- 4.3 Worked examples -- Exact solution -- FEM solution -- 4.3.1 Properties of the FEM -- 4.3.1.1 Reproduction property of the FEM -- 4.3.1.2 Convergence property of the FEM -- 4.3.1.3 Rate of convergence of FEM results -- Step 1: Obtaining the direction cosines of the elements -- Step 2: Calculation of element matrices in the global coordinate system -- Step 3: Assembly of global FE matrices -- Step 4: Applying boundary conditions -- Step 5: Solving the FE matrix equation -- 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 -- Step 1: Obtaining the element matrices.

Step 2: Applying boundary conditions -- Step 3: Solving the FE matrix equation -- 5.5 Case study: resonant frequencies of micro-resonant transducer -- 5.5.1 Modeling -- 5.5.2 ABAQUS input file -- 5.5.3 Solution process -- 5.5.4 Results and discussion -- 5.5.5 Comparison with ANSYS -- 5.6 Review questions -- 6 FEM for Frames -- 6.1 Introduction -- 6.2 FEM equations for planar frames -- 6.2.1 The idea of superposition -- 6.2.2 Equations in the local coordinate system -- 6.2.3 Equations in the global coordinate system -- 6.3 FEM equations for space frames -- 6.3.1 Equations in the local coordinate system -- 6.3.2 Equations in the global coordinate system -- 6.4 Remarks -- 6.5 Case study: finite element analysis of a bicycle frame -- 6.5.1 Modeling -- 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 Elements for axisymmetric structures -- 7.6 Higher order elements-triangular element family -- 7.6.1 General formulation of shape functions -- 7.6.2 Quadratic triangular elements -- 7.6.3 Cubic triangular elements -- 7.7 Rectangular Elements -- 7.7.1 Lagrange type elements -- 7.7.2 Serendipity type elements -- 7.8 Elements with curved edges -- 7.9 Comments on Gauss integration -- 7.10 Case study: Side drive micro-motor -- 7.10.1 Modeling -- 7.10.2 ABAQUS input file.

7.10.3 Solution process -- 7.10.4 Results and discussion -- 7.11 Review questions -- 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 The idea of superposition -- 8.3.2 Elements in the local coordinate system -- 8.3.3 Elements in the global coordinate system -- 8.4 Remarks -- 8.5 Case study: Natural frequencies of the micro-motor -- 8.5.1 Modeling -- 8.5.2 ABAQUS input file -- 8.5.3 Solution process -- 8.5.4 Results and discussion -- 8.6 Case study: Transient analysis of a micro-motor -- 8.6.1 Modeling -- 8.6.2 Abaqus input file -- 8.6.3 Solution process -- 8.6.4 Results and discussion -- 8.7 Review questions -- 9 FEM for 3D Solid Elements -- 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 -- 9.4.2.1 Lagrange type elements -- 9.4.2.2 Serendipity type elements -- 9.5 Elements with curved surfaces -- 9.6 Case study: Stress and strain analysis of a quantum dot heterostructure -- 9.6.1 Modeling -- Meshing -- Material properties -- Constraints and boundary conditions -- 9.6.2 ABAQUS input file -- 9.6.3 Solution process -- 9.6.4 Results 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 elements formulated by mapping -- 10.3.2 Gradual damping elements -- 10.3.3 Coupling of FEM and the boundary element method -- 10.3.4 Coupling of FEM and the strip element method -- 10.4 Finite strip elements -- 10.5 Strip element method -- 10.6 Meshfree methods -- 10.7 S-FEM.

11 Modeling Techniques -- 11.1 Introduction -- 11.2 CPU time estimation -- 11.3 Geometry modeling -- 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 Modeling of offsets -- 11.7.1 Methods for modeling offsets -- 11.7.2 Creation of MPC equations for offsets -- 11.8 Modeling of supports -- 11.9 Modeling of joints -- 11.10 Other applications of MPC equations -- 11.10.1 Modeling of symmetric boundary conditions -- 11.10.2 Enforcement of mesh compatibility -- 11.10.3 Modeling 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 composite wall -- 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 Composite wall -- 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(e) -- 12.4.5 Point heat source or sink -- 12.5 Summary -- 12.6 Case study: Temperature distribution of heated road surface -- 12.6.1 Modeling -- 12.6.2 ABAQUS input file.

12.6.3 Results and discussion.