The following files are provided to give background in the mathematical aspects of the course.
| 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 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) |
