Special software is required to use some of the files in this section: .nb.
The following files are provided to give background in the mathematical aspects of the course.
Tool files
| Lec # |
Topics |
tools |
| Part 1: Review of the Equations of Linear Elasticity |
| 1 |
Introduction |
Math Tutorial (NB) |
| 4 |
Kinematics
Strain at a Point
Transformation of Stress Components
Compatibility Conditions |
Influence of Nonlinear Strains (NB) |
| Part 2: Energy and Variational Principles |
| 15 |
Energy Theorems of Structural Mechanics
Castigliano's First Theorem
Castigliano's Second Theorem
Betti's and Maxwell's Reciprocity Theorems |
Castigliano's Theorem Example (NB) |
| 17-18 |
The Ritz Method
Description of the Method
Matrix Form of the Ritz Equations
One Dimensional Examples |
The Ritz Method: Beam Example (NB)
Space Elevators (NB) |
| 20-22 |
Formulation of the Displacement Based Finite Element Method
General Derivation of Finite Element Equilibrium Equations
Imposition of Displacement Boundary Conditions
Generalized Coordinate Models for Specific Problems
Lumping of Structure Properties and Loads |
Notes on The Finite Element Method II (NB)
Fixes to the Ritz Method (NB)
Application to Rods (NB)
The Beam Model (NB) |
| 23 |
Convergence of Analysis Results
Definition of Convergence
Properties of the Finite Element Solution
Rate of Convergence
Calculation of Stresses and the Assessment of Error |
2nd Plane Stress Element (NB)
Isoparametric 4-node 2nd Element (NB) |
| 30 |
Numerical Integration |
Quadtrature (NB) |