EN224: Linear Elasticity          

   Division of Engineering
    Brown University

Lecture Notes, Spring 2005

 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

3. 3D Static Boundary Value 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

7. Complex Variable Methods for Plane Elastostatics

8. Energy Theorems and Applications

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