Example Problems


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 crystal
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 Solid
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