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 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 Uniqueness Theorems
2.3 Reciprocal Theorem
2.4 Saint Venant's Principle

 

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

 

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 materials

9.1 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