Introduction Physical Problems in Engineering Numerical Techniques: Practical Solution Tools Why S-FEM? The Idea of S-FEM Key Techniques Used in S-FEM S-FEM Models and Properties Some Historical Notes Outline of the Book Basic Equations for Solid Mechanics Equilibrium Equation: In Stresses Constitutive Equation Compatibility Equation Equilibrium Equation: In Displacements Equations in Matrix Form Boundary Conditions Some Standard Default Conventions and Notations The Finite Element Method General Procedure of FEM Proper Spaces Weak Formulation and Properties of the Solution Domain Discretization: Creation of Finite-Dimensional Space Creation of Shape Functions Displacement Function Creation Strain Evaluation Formulation of the Discretized System of Equations FEM Solution: Existence, Uniqueness, Error, and Convergence Some Other Properties of the FEM Solution Linear Triangular Element (T3) Four-Node Quadrilateral Element (Q4) Four-Node Tetrahedral Element (T4) Eight-Node Hexahedral Element (H8) Gauss Integration Fundamental Theories for S-FEM General Procedure for S-FEM Models Domain Discretization with Polygonal Elements Creating a Displacement Field: Shape Function Construction Evaluation of the Compatible Strain Field Modify/Construct the Strain Field Minimum Number of Smoothing Domains: Essential to Stability Smoothed Galerkin Weak Form Discretized Linear Algebraic System of Equations Solve the Algebraic System of Equations Error Assessment in S-FEM and FEM Models Implementation Procedure for S-FEM Models General Properties of S-FEM Models Cell-Based Smoothed FEM Cell-Based Smoothing Domain Discretized System of Equations Shape Function Evaluation Some Properties of CS-FEM Stability of CS-FEM and nCS-FEM Standard Patch Test: Accuracy Selective CS-FEM: Volumetric Locking Free Numerical Examples Node-Based Smoothed FEM Introduction Creation of Node-Based Smoothing Domains Formulation of NS-FEM Evaluation of Shape Function Values Properties of NS-FEM An Adaptive NS-FEM Using Triangular Elements Numerical Examples Edge-Based Smoothed FEM Introduction Creation of Edge-Based Smoothing Domains Formulation of the ES-FEM Evaluation of the Shape Function Values in the ES-FEM A Smoothing-Domain-Based Selective ES/NS-FEM Properties of the ES-FEM Numerical Examples Face-Based Smoothed FEM Introduction Face-Based Smoothing Domain Creation Formulation of FS-FEM-T4 A Smoothing-Domain-Based Selective FS/NS-FEM-T4 Model Stability, Accuracy, and Mesh Sensitivity Numerical Examples The αFEM Introduction Idea of αFEM-T3 and αFEM-T4 αFEM-T3 and αFEM-T4 for Nonlinear Problems Implementation and Patch Tests Numerical Examples S-FEM for Fracture Mechanics Introduction Singular Stress Field Creation at the Crack-Tip Possible sS-FEM Methods sNS-FEM Models sES-FEM Models Stiffness Matrix Evaluation J-Integral and SIF Evaluation Interaction Integral Method for Mixed Mode Numerical Examples Solved Using sES-FEM-T3 Numerical Examples Solved Using sNS-FEM-T3 S-FEM for Viscoelastoplasticity Introduction Strong Formulation for Viscoelastoplasticity FEM for Viscoelastoplasticity: A Dual Formulation S-FEM for Viscoelastoplasticity: A Dual Formulation A PosterioriError Estimation Numerical Examples ES-FEM for Plates Introduction Weak Form for the Reissner-Mindlin Plate FEM Formulation for the Reissner-Mindlin Plate ES-FEM-DSG3 for the Reissner-Mindlin Plate Numerical Examples: Patch Test Numerical Examples: Static Analysis Numerical Examples: Free Vibration of Plates Numerical Examples: Buckling of Plates S-FEM for Piezoelectric Structures Introduction Galerkin Weak Form for Piezoelectrics Finite Element Formulation for the Piezoelectric Problem S-FEM for the Piezoelectric Problem Numerical Results S-FEM for Heat Transfer Problems Introduction Strong-Form Equations for Heat Transfer Problems Boundary Conditions Weak Forms for Heat Transfer Problems FEM Equations S-FEM Equations Evaluation of the Smoothed Gradient Matrix Numerical Example Bioheat Transfer Problems S-FEM for Acoustics Problems Introduction Mathematical Model of Acoustics Problems Weak Forms for Acoustics Problems FEM Equations S-FEM Equations Error in a Numerical Model Numerical Examples Index References appear at the end of each chapter. amp;lt;BR>Creation of Shape Functions Displacement Function Creation Strain Evaluation Formulation of the Discretized System of Equations FEM Solution: Existence, Uniqueness, Error, and Convergence Some Other Properties of the FEM Solution Linear Triangular Element (T3) Four-Node Quadrilateral Element (Q4) Four-Node Tetrahedral Element (T4) Eight-Node Hexahedral Element (H8) Gauss Integration Fundamental Theories for S-FEM General Procedure for S-FEM Models Domain Discretization with Polygonal Elements Creating a Displacement Field: Shape Function Construction Evaluation of the Compatible Strain Field Modify/Construct the Strain Field Minimum Number of Smoothing Domains: Essential to Stability Smoothed Galerkin Weak Form Discretized Linear Algebraic System of Equations Solve the Algebraic System of Equations Error Assessment in S-FEM and FEM Models Implementation Procedure for S-FEM Models General Properties of S-FEM Models Cell-Based Smoothed FEM Cell-Based Smoothing Domain Discretized System of Equations Shape Function Evaluation Some Properties of CS-FEM Stability of CS-FEM and nCS-FEM Standard Patch Test: Accuracy Selective CS-FEM: Volumetric Locking Free Numerical Examples Node-Based Smoothed FEM Introduction Creation of Node-Based Smoothing Domains Formulation of NS-FEM Evaluation of Shape Function Values Properties of NS-FEM An Adaptive NS-FEM Using Triangular Elements Numerical Examples Edge-Based Smoothed FEM Introduction Creation of Edge-Based Smoothing Domains Formulation of the ES-FEM Evaluation of the Shape Function Values in the ES-FEM A Smoothing-Domain-Based Selective ES/NS-FEM Properties of the ES-FEM Numerical Examples Face-Based Smoothed FEM Introduction Face-Based Smoothing Domain Creation Formulation of FS-FEM-T4 A Smoothing-Domain-Based Selective FS/NS-FEM-T4 Model Stability, Accuracy, and Mesh Sensitivity Numerical Examples The αFEM Introduction Idea of αFEM-T3 and αFEM-T4 αFEM-T3 and αFEM-T4 for Nonlinear Problems Implementation and Patch Tests Numerical Examples S-FEM for Fracture Mechanics Introduction Singular Stress Field Creation at the Crack-Tip Possible sS-FEM Methods sNS-FEM Models sES-FEM Models Stiffness Matrix Evaluation J-Integral and SIF Evaluation Interaction Integral Method for Mixed Mode Numerical Examples Solved Using sES-FEM-T3 Numerical Examples Solved Using sNS-FEM-T3 S-FEM for Viscoelastoplasticity Introduction Strong Formulation for Viscoelastoplasticity FEM for Viscoelastoplasticity: A Dual Formulation S-FEM for Viscoelastoplasticity: A Dual Formulation A PosterioriError Estimation Numerical Examples ES-FEM for Plates Introduction Weak Form for the Reissner-Mindlin Plate FEM Formulation for the Reissner-Mindlin Plate ES-FEM-DSG3 for the Reissner-Mindlin Plate Numerical Examples: Patch Test Numerical Examples: Static Analysis Numerical Examples: Free Vibration of Plates Numerical Examples: Buckling of Plates S-FEM for Piezoelectric Structures Introduction Galerkin Weak Form for Piezoelectrics Finite Element Formulation for the Piezoelectric Problem S-FEM for the Piezoelectric Problem Numerical Results S-FEM for Heat Transfer Problems Introduction Strong-Form Equations for Heat Transfer Problems Boundary Conditions Weak Forms for Heat Transfer Problems FEM Equations S-FEM Equations Evaluation of the Smoothed Gradient Matrix Numerical Example Bioheat Transfer Problems S-FEM for Acoustics Problems Introduction Mathematical Model of Acoustics Problems Weak Forms for Acoustics Problems FEM Equations S-FEM Equations Error in a Numerical Model Numerical Examples Index References appear at the end of each chapter. aic System of Equations Solve the Algebraic System of Equations Error Assessment in S-FEM and FEM Models Implementation Procedure for S-FEM Models General Properties of S-FEM Models Cell-Based Smoothed FEM Cell-Based Smoothing Domain Discretized System of Equations Shape Function Evaluation Some Properties of CS-FEM Stability of CS-FEM and nCS-FEM Standard Patch Test: Accuracy Selective CS-FEM: Volumetric Locking Free Numerical Examples Node-B.