Example Problems   Download problems:   Problems by chapter in html format ```1. Objectives and Applications of Solid Mechanics 1.1 Defining a Problem in Solid Mechanics ``` ```2. Governing Equations 2.1 Mathematical Description of Shape Changes in Solids``` ``` 2.2 Mathematical Description of Internal Forces in Solids 2.3 Equations of motion and equilibrium for deformable solids 2.4 Work done by stresses; Principle of Virtual Work 3. Constitutive Equations: Relations between Stress and Strain``` ``` 3.1 General Requirements for Constitutive Equations 3.2 Linear Elastic Material Behavior ``` ` 3.3 Hypoelasticity - elasticity with nonlinear stress-strain behavior ` ` 3.4 Generalized Hooke’s law – elastic materials subjected to small stretches but large rotations` ` 3.5 Hyperelasticity - time independent behavior of rubbers and foams subjected to large strains ` ` 3.6 Viscoelasticity - time dependent behavior of polymers at small strains ` ` 3.7 Small strain, rate independent plasticity - metals loaded beyond yield ` ` 3.8 Small strain viscoplasticity - creep and high rate deformation of metals ` ` 3.9 Large strain, rate dependent plasticity ` ` 3.10 Large strain viscoelasticity ` ` 3.11 Critical State Models for Soils` ` 3.12 Constitutive models for metal single crystals` ` 3.13 Constitutive models for contacting surfaces and interfaces in solids` ` ` ```4. Solutions to simple boundary and initial value problems 4.1 Axially & Spherically Symmetric Solutions for Linear Elastic Solids Under Quasi-Static Loading``` ` 4.2 Axially & Spherically Symmetric Solutions for Elastic-Plastic Solids Under Quasi-Static Loading` ` 4.3 Spherically Symmetric Solution for Large Strain Elasticity Problems ` ` 4.4 Simple Dynamic Solutions for Linear Elastic Solids ` ` ` ```5. Analytical Techniques and Solutions for Linear Elastic Solids 5.1 General Principles ``` ` 5.2 Airy Function Solutions to Plane Stress and Plane Strain Problems for Linear Elastic Solids ` ` 5.3 Complex Variable Solution to Plane Strain Static Elasticity Problems ` ` 5.4 Solutions to 3D Static Elasticity Problems ` ` 5.5 Solutions to Plane Problems for Anisotropic Elastic Solids ` ` 5.6 Solutions to Dynamic Problems for Isotropic Elastic Solids ` ` 5.7 Energy Methods for Solving Static Linear Elasticity Problems ` ` 5.8 The Reciprocal Theorem and its Applications ` ` 5.9 Energetics of Dislocations in Elastic Solids` ` 5.10 Rayleigh-Ritz Method for Estimating Natural Frequencies ` ` ` ```6. Analytical Techniques and Solutions for Plastic Solids 6.1 Slip Line Field Theory ``` ``` 6.2 Bounding Theorems in Plasticity and their Applications ``` ` ` ```7. Introduction to Finite Element Analysis in Solid Mechanics 7.1 A Guide to Using Finite Element Software ``` ``` 7.2 A Simple Finite Element Program ``` ` ` ```8. Theory and Implementation of the Finite Element Method 8.1 Generalized FEA for Static Linear Elasticity ``` ` 8.2 The Finite Element Method for Dynamic Linear Elasticity ` ` 8.3 The Finite Element Method for Nonlinear (Hypoelastic) Materials ` ` 8.4 The Finite Element Method for Large Deformations: Hyperelasticity ` ` 8.5 The Finite Element Method for Viscoplasticity ` ` 8.6 Advanced Element Formulations: Incompatible Modes; Reduced Integration and Hybrid Elements` ` ` ```9. Modeling Material Failure 9.1 Summary of Mechanisms of Fracture and Fatigue under Static and Cyclic Loading ``` ` 9.2 Stress and Strain Based Failure Criteria ` ` 9.3 Modeling Failure by Crack Growth: Linear Elastic Fracture Mechanics ` ` 9.4 Energy Methods in Fracture Mechanics ` ` 9.5 Plastic Fracture Mechanics ` ``` 9.6 Linear Elastic Fracture Mechanics for Interfaces ``` ` ` ```10. Approximate Theories for Solids with Special Shapes: Rods, Beams, Plates and Shells 10.1 Preliminaries: Dyadic Notation for Vectors and Tensors ``` ` 10.2 Motion and Deformation of Slender Rods ` ` 10.3 Simplified Versions of the General Theory of Deformable Rods ` ` 10.4 Exact Solutions to Simple Problems Involving Elastic Rods ` ` 10.5 Motion and Deformation of Thin Shells: General Theory ` ` 10.6 Simplified Versions of the General Shell Theory` ``` 10.7 Solutions to Problems Involving Membranes, Plates and Shells ``` `Appendix A: Review of Vectors and Matrices ` `Appendix B: A Brief Introduction to Tensors and their Properties ` `Appendix C: Index Notation for Vector and Tensor Operations ` `Appendix D: Vector and Tensor Operations in Polar Coordinates ` `Appendix E: Miscellaneous Derivations ` ` ` ` ` ` `