Courses:

Techniques for Structural Analysis and Design >> Content Detail



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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.


Lec #Topicstools
Part 1: Review of the Equations of Linear Elasticity
1IntroductionMath Tutorial (NB)
4Kinematics

Strain at a Point

Transformation of Stress Components

Compatibility Conditions
Influence of Nonlinear Strains (NB)
Part 2: Energy and Variational Principles
15Energy Theorems of Structural Mechanics

Castigliano's First Theorem

Castigliano's Second Theorem

Betti's and Maxwell's Reciprocity Theorems
Castigliano's Theorem Example (NB)
17-18The Ritz Method

Description of the Method

Matrix Form of the Ritz Equations

One Dimensional Examples
The Ritz Method: Beam Example (NB)

Space Elevators (NB)
20-22Formulation 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)
23Convergence 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)
30Numerical IntegrationQuadtrature (NB)

 








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