Computational Solid Mechanics: Variational Formulation and High Order Approximation

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