** EN224: Linear Elasticity **

** Division of Engineering
Brown University**

** These notes
were written by Professor Allan Bower,
Division of Engineering, Brown University, Providence RI 02912.
You are welcome to read or print them for your own personal use. All other
rights are reserved.**

**You may also find the general introductory solid mechanics
text posted at http://solidmechanics.org
useful. This text contains extensive materials on elasticity, plasticity,
constitutive models, FEA, beams, plates and shells, as well as more than 400
practice problems.**

1. Review of the Field Equations of Linear Elasticity1.1 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

3. 3D Static Boundary Value Problems

3.1 Papkovich Neuber Potentials

3.2 Singular Solutions for an Infinite
Solid

3.3 The Boundary Element Method

3.4 Solutions for 3D dislocation loops in
an infinite solid

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 Solving Saint-Venant Torsion
Problems using Warping Functions

4.3 Solving Torsion Problems
using Prandtl Stress Functions

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

5.1 Field Equations and Boundary
Conditions

5.2 Complex Variable Solutions
to Anti-Plane Shear Problems

5.3 Solving Anti-Plane Shear
Problems Using Taylor and Laurent Series

5.4 Solving Anti-Plane Shear
Problems Using the Cauchy Integral Formulae

5.5 Solving Anti-Plane Shear Problems
Using Conformal Mapping

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

6.1 Plane Strain Approximation

6.2 Plane Stress Approximation

6.3 Field Equations Implied by the Fundamental
2D System

6.4 Solving Plane Problems Using Airy Functions

6.5 Examples Using Airy Stress Functions

7. Complex Variable Methods for Plane Elastostatics

7.1 Complex Variable Representation
of Plane Elastostatic Solutions

7.2 Boundary Conditions on Complex
Potentials

7.3 Simple Examples of Complex Potentials

7.4 Solving Plane Problems Using Taylor
and Laurent Series

7.5 Solving Plane Problems Using the
Cauchy Integral Formula

7.6 Solving Half-Plane Problems Using
Analytic Continuation

7.7 Traction Boundary Value Problems
for the Half Plane

7.8 Mixed Boundary Value Problems
for the Half Plane: Contact and crack problems

8. Energy Theorems and Applications

8.1 The Principle of Virtual Work

8.2 The Principles of Stationary and
Minimum Potential Energy

8.3 Applications of Stationary and
Minimum Potential Energy I: Approximate Solutions

8.4 Applications of Stationary and
Minimum Potential Energy II: Bounds and Comparisons

8.5 The Principles of Stationary and
Minimum Complementary Energy

8.6 Applications of Minimum Complementary
Energy

9. Elasticity theory for anisotropic materials9.1 General Principles: Constitutive law and field equations for anisotropic materials

9.2 Anti-plane shear solutions for anisotropic materials

9.3 The Stroh representation for general plane deformation of anisotropic materials

9.4 Solutions to selected boundary value problems for anisotropic materials