EN224: Linear Elasticity

Division of Engineering

Course Outline, Fall 1997-98

1. Review of the Field Equations of Linear Elasticity

1.1 Kinematics of Deformable Solids
1.2 Kinetics of Deformable Solids
1.3 Constitutive Models for Elastic Materials
1.4 Summary of Linearized Field Equations; Boundary and Initial Value Problems
1.5 Field Equations Implied by the Fundamental System

2. Theorems of Linear Elasticity

2.1 Superposition
2.2 Existence and Uniqueness Theorems
2.3 Reciprocal Theorem

3. 3D Static Boundary Value Problems

3.1 Papkovich Neuber Potentials
3.2 Singular Solutions for an Infinite Solid
3.3 Solutions for 3D dislocation loops in an infinite solid
3.4 The Boundary Element Method
3.5 Eigenstrains
3.6 Eshelby Inclusion Problems
3.7 Singular Solutions for the Half Space
3.8 Contact Problems

4. 2D Static Boundary Value Problems I: Saint Venant Theory of Torsion

4.1 General Saint-Venant Theory of Slender Members
4.2 Field Equations and Boundary Conditions for Saint Venant Torsion
4.3 Solution via Warping Functions

5. 2D Static Boundary Value Problems II: Anti-Plane Shear

5.1 Field Equations and Boundary Conditions
5.2 Example Problems

6. 2D Static Boundary Value Problems III: Plane Elasticity

6.1 Plane Strain Approximation
6.2 Plane Stress Approximation
6.3 Summary of Field Equations
6.4 Stress Equations of Compatibility
6.5 Solution of Plane Problems using Airy Stress Functions

7. Complex Variable Methods for Plane Elastostatics

7.1 Review of Complex Variables
7.2 Complex Variable Representation of Plane Elastostatic Solutions
7.3 Boundary Conditions on Complex Potentials
7.4 Series Solutions for Complex Potentials
7.5 Application of the Cauchy Integral Formula
7.6 Conformal Mapping

8. Energy Theorems and Applications

8.1 Principle of Minimum Potential Energy
8.2 Approximate Solutions Obtained Using Energy Methods
8.3 Bounds and Comparison Theorems Derived Using Energy Methods
8.4 Principle of Minimum Complementary Energy