Computational Solid Mechanics : Variational Formulation and High Order Approximation

Presents a Systematic Approach for Modeling Mechanical Models Using Variational Formulation-Uses Real-World Examples and Applications of Mechanical ModelsUtilizing material developed in a classroom setting and tested over a 12-year period, Computational Solid Mechanics: Variational Formulation and High-Order Approximation details an approach that e Content: INTRODUCTION Initial Aspects Bars Shafts Beams Two-dimensional Problems Plates Linear Elastic Solids EQUILIBRIUM OF PARTICLES AND RIGID BODIES Introduction Diagrammatic Conventions Equilibrium of Particles Equilibrium of Rigid Bodies Principle of Virtual Power (PVP) Some aspects about the definition of power Final comments Problems FORMULATION AND APPROXIMATION OF BARS Introduction Kinematics Strain Measure Rigid actions Determination of Internal Loads Determination of External Loads Equilibrium Material Behavior Application of the Constitutive Equation Design and Verification Bars Subjected to Temperature Changes Volume and Area Strain Measures Singularity Functions for External Loading Representation Summary of the Variational Formulation of Bars Approximated Solution Finite Element Method (FEM) Analysis of Trusses Final Comments Problems FORMULATION AND APPROXIMATION OF SHAFTS Introduction Kinematics Strain Measure Rigid Actions Determination of Internal Loads Determination of External Loads Equilibrium Material Behavior Application of the Constitutive Equation Design and Verification Singularity Functions for External Loading Representation Summary of the Variational Formulation of Shafts Approximated Solution Mathematical Aspects of the FEM Local Coordinate Systems One-dimensional Shape Functions Mapping Numerical Integration Collocation Derivative Final Comments Problems FORMULATION AND APPROXIMATION OF BEAMS IN BENDING Introduction Kinematics Strain Measure Rigid Actions Determination of Internal Loads Determination of External Loads Equilibrium Application of the Constitutive Equation Design and Verification Singularity Functions for External Loading Representation Summary of the Variational Formulation for the Euler-Bernouilli Beam Buckling of Columns Euler Column Approximation of the Euler-Bernouilli Beam High Order Beam Element Mathematical Aspects of the FEM Final Comments Problems FORMULATION AND APPROXIMATION OF BEAM WITH SHEAR Introduction Kinematics Strain Measure Rigid Actions Determination of Internal Loads Determination of External Loads Equilibrium Application of the Constitutive Equation Shear Stress Distribution Design and Verification Standardized Cross Section Shapes Shear Center Summary of the Variational Formulation of Beams with Shear Energy Methods Approximation of the Timoshenko Beam Mathematical Aspects of the FEM Final Comments Problems FORMULATION AND APPROXIMATION OF D AND D BEAMS Introduction Two-dimensional Beam Three-dimensional Beam BeamLab Program Summary of the Variational Formulation of Beams Approximation of Beams Final Comments Exercises FORMULATION AND APPROXIMATION OF SOLIDS Introduction Kinematics Strain Measures Rigid Actions Determination of Internal Loads Determination of External Loads Equilibrium Generalized Hooke Law Application of the Constitutive Equation Formulation Employing Tensors Verification of Linear Elastic Solids Approximation of Linear Elastic Solids Final Comments Problems FORMULATION AND APPROXIMATION OF PLANE STATE PROBLEMS Plane Stress State Plane Strain State Compatibility Equations Analytical Solutions for Plane Problems in Elasticity Analytical Solutions for Problems in Three-dimensional Elasticity Plane State Approximation (hp)fem program Twist of Generic Sections Multi-dimensional Numerical Integration Summary of the Variational Formulation of Mechanical Models Final Comments Problems FORMULATION AND APPROXIMATION OF PLATES IN BENDING Introduction Kinematics Strain Measures Rigid Actions Determination of Internal Loads Determination of External Loads Equilibrium Application of the Constitutive Equation Approximation of the Kirchhoff Plate Exercises References Front Cover 1 Dedication 6 Contents 8 Chapter 1: INTRODUCTION 30 Chapter 2: EQUILIBRIUM OF PARTICLES AND RIGID BODIES 44 Chapter 3: FORMULATION AND APPROXIMATION OF BARS 74 Chapter 4: FORMULATION AND APPROXIMATION OF SHAFTS 156 Chapter 5: FORMULATION AND APPROXIMATION OF BEAMS 232 Chapter 6: FORMULATION AND APPROXIMATION OF BEAM IN SHEAR 320 Chapter 7: FORMULATION AND APPROXIMATION OF TWO/THREE-DIMENSIO-NAL BEAMS 388 Chapter 8: FORMULATION AND APPROXIMATION OF SOLIDS 468 Chapter 9: FORMULATION AND APPROXIMATION OF PLANE PROBLEMS 576 Chapter 10: FORMULATION AND APPROXIMATION OF PLATES 632 References 668